Subgroups — C₃²×#3067 #11770116

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#575	C₂	1	2	yes	maximal, complemented
2	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#473	C₂	1	2	yes	maximal, complemented
5	C₃²×#472	C₂	1	2	yes	maximal, complemented
6	C₃²×#471	C₂	1	4	yes	maximal, complemented
7	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#413	C₂	1	2	yes	maximal, complemented
9	C₃×#3067	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
11	C₂×C₃²×#41	C₂²	1	2	yes	—
12	C₃²×#137	—	2	2	no	—
13	C₃²×#137	C₂²	1	4	yes	—
14	C₃²×AGL(1,ℤ/8)	—	2	2	no	—
15	C₃²×AGL(1,ℤ/8)	C₂²	1	4	yes	—
16	C₃²×#135	—	2	4	no	—
17	C₃²×#135	—	2	1	no	—
18	C₃²×#135	—	2	1	no	—
19	C₃²×#135	—	2	1	no	—
20	C₃²×#135	—	2	1	no	—
21	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×SD₁₆	C₂²	1	2	yes	complemented
23	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
24	C₃²×#131	—	2	1	no	—
25	C₃²×#131	—	2	1	no	—
26	C₃²×#131	C₂²	1	2	yes	—
27	C₃²×#131	C₂²	1	2	yes	—
28	C₂×C₃²×M₁₆	—	2	1	no	—
29	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
31	C₂²×C₃²×C₈	—	2	1	no	—
32	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
33	C₃²×#108	C₂²	1	2	yes	complemented
34	C₃²×#108	C₂²	1	2	yes	complemented
35	C₃²×#101	C₂²	1	4	yes	complemented
36	C₃²×#100	C₂²	1	4	yes	complemented
37	C₃×#575	C₂×C₃	1	8	yes	complemented
38	C₂×C₃×#135	C₂×C₃	1	4	yes	complemented
39	C₂×C₃×#131	C₂×C₃	1	4	yes	complemented
40	C₃×#473	C₂×C₃	1	8	yes	complemented
41	C₃×#472	C₂×C₃	1	8	yes	complemented
42	C₃×#471	C₂×C₃	1	16	yes	complemented
43	C₂×C₃×#108	C₂×C₃	1	4	yes	complemented
44	C₃×#413	C₂×C₃	1	8	yes	complemented
45	C₃²×#41	—	2	1	no	—
46	C₃²×#41	—	2	1	no	—
47	C₃²×#41	—	2	2	no	—
48	C₃²×#41	—	2	2	no	—
49	C₃²×#41	—	2	2	no	—
50	C₃²×#41	—	2	2	no	—
51	C₃²×#41	D₄	1	2	yes	—
52	C₃²×#41	C₂³	1	2	yes	—
53	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
54	C₂×C₃²×Q₈	C₂³	1	2	yes	—
55	C₂×C₃²×D₄	—	2	1	no	—
56	C₂×C₃²×D₄	—	2	2	no	—
57	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
58	C₂×C₃²×D₄	C₂³	1	2	yes	—
59	C₂²×C₃²×C₄	—	2	1	no	—
60	C₂²×C₃²×C₄	—	2	2	no	—
61	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
62	C₃²×Q₁₆	—	2	4	no	—
63	C₃²×Q₁₆	—	2	1	no	—
64	C₃²×Q₁₆	—	2	1	no	—
65	C₃²×SD₁₆	—	2	4	no	—
66	C₃²×SD₁₆	—	2	4	no	—
67	C₃²×SD₁₆	—	2	2	no	—
68	C₃²×SD₁₆	—	2	2	no	—
69	C₃²×D₈	—	2	4	no	—
70	C₃²×D₈	—	2	1	no	—
71	C₃²×D₈	—	2	1	no	—
72	C₃²×M₁₆	—	2	1	no	—
73	C₃²×M₁₆	—	2	2	no	—
74	C₃²×M₁₆	—	2	2	no	—
75	C₃²×M₁₆	—	2	2	no	—
76	C₃²×M₁₆	C₂³	1	2	yes	—
77	C₃²×M₁₆	C₂³	1	4	yes	—
78	C₂×C₃²×C₈	—	2	1	no	—
79	C₂×C₃²×C₈	—	2	2	no	—
80	C₂×C₃²×C₈	—	2	2	no	—
81	C₂×C₃²×C₈	—	2	2	no	—
82	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
83	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
84	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
85	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
86	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
88	#3067	C₃²	1	1	yes	characteristic, direct product factor, Sylow
89	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
90	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
91	C₃×#137	—	2	8	no	—
92	C₃×#137	C₂²×C₃	1	16	yes	—
93	C₃×AGL(1,ℤ/8)	—	2	8	no	—
94	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	16	yes	—
95	C₃×#135	—	2	16	no	—
96	C₃×#135	—	2	4	no	—
97	C₃×#135	—	2	4	no	—
98	C₃×#135	—	2	4	no	—
99	C₃×#135	—	2	4	no	—
100	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
101	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	complemented
102	C₂×C₃×D₈	C₂²×C₃	1	4	yes	complemented
103	C₃×#131	—	2	4	no	—
104	C₃×#131	—	2	4	no	—
105	C₃×#131	C₂²×C₃	1	8	yes	—
106	C₃×#131	C₂²×C₃	1	8	yes	—
107	C₂×C₃×M₁₆	—	2	4	no	—
108	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
109	C₂×C₃×M₁₆	C₂²×C₃	1	8	yes	—
110	C₂²×C₃×C₈	—	2	4	no	—
111	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
112	C₃×#108	C₂²×C₃	1	8	yes	complemented
113	C₃×#108	C₂²×C₃	1	8	yes	complemented
114	C₃×#101	C₂²×C₃	1	16	yes	complemented
115	C₃×#100	C₂²×C₃	1	16	yes	complemented
116	C₂³×C₃²	—	2	1	no	—
117	C₂³×C₃²	—	2	2	no	—
118	C₂³×C₃²	#41	1	1	yes	characteristic
119	C₃²×Q₈	—	2	1	no	—
120	C₃²×Q₈	—	2	2	no	—
121	C₃²×Q₈	—	2	2	no	—
122	C₃²×Q₈	C₂×D₄	1	2	yes	—
123	C₃²×D₄	—	2	2	no	—
124	C₃²×D₄	—	2	2	no	—
125	C₃²×D₄	—	2	1	no	—
126	C₃²×D₄	—	2	2	no	—
127	C₃²×D₄	—	2	2	no	—
128	C₃²×D₄	—	4	2	no	—
129	C₃²×D₄	—	4	2	no	—
130	C₃²×D₄	C₂×D₄	1	2	yes	—
131	C₂×C₃²×C₄	—	2	1	no	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	—	2	2	no	—
134	C₂×C₃²×C₄	—	2	2	no	—
135	C₂×C₃²×C₄	—	4	2	no	—
136	C₂×C₃²×C₄	—	4	2	no	—
137	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	#41	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
143	C₃²×C₈	—	2	2	no	—
144	C₃²×C₈	—	2	4	no	—
145	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
146	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
147	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
148	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
149	#575	C₂×C₃²	1	2	yes	complemented
150	C₂×#135	C₂×C₃²	1	1	yes	characteristic, complemented
151	C₂×#131	C₂×C₃²	1	1	yes	characteristic, complemented
152	#473	C₂×C₃²	1	2	yes	complemented
153	#472	C₂×C₃²	1	2	yes	complemented
154	#471	C₂×C₃²	1	4	yes	complemented
155	C₂×#108	C₂×C₃²	1	1	yes	characteristic, complemented
156	#413	C₂×C₃²	1	2	yes	complemented
157	C₃×#41	—	2	4	no	—
158	C₃×#41	—	2	4	no	—
159	C₃×#41	—	2	8	no	—
160	C₃×#41	—	2	8	no	—
161	C₃×#41	—	2	8	no	—
162	C₃×#41	—	2	8	no	—
163	C₃×#41	C₃×D₄	1	8	yes	—
164	C₃×#41	C₂³×C₃	1	8	yes	—
165	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
166	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂×C₃×D₄	—	2	8	no	—
169	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
170	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	2	8	no	—
173	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
174	C₃×Q₁₆	—	2	16	no	—
175	C₃×Q₁₆	—	2	4	no	—
176	C₃×Q₁₆	—	2	4	no	—
177	C₃×SD₁₆	—	2	16	no	—
178	C₃×SD₁₆	—	2	16	no	—
179	C₃×SD₁₆	—	2	8	no	—
180	C₃×SD₁₆	—	2	8	no	—
181	C₃×D₈	—	2	16	no	—
182	C₃×D₈	—	2	4	no	—
183	C₃×D₈	—	2	4	no	—
184	C₃×M₁₆	—	2	4	no	—
185	C₃×M₁₆	—	2	8	no	—
186	C₃×M₁₆	—	2	8	no	—
187	C₃×M₁₆	—	2	8	no	—
188	C₃×M₁₆	C₂³×C₃	1	8	yes	—
189	C₃×M₁₆	C₂³×C₃	1	16	yes	—
190	C₂×C₃×C₈	—	2	4	no	—
191	C₂×C₃×C₈	—	2	8	no	—
192	C₂×C₃×C₈	—	2	8	no	—
193	C₂×C₃×C₈	—	2	8	no	—
194	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
195	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
196	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
197	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
198	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
199	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	—	4	1	no	—
202	C₂²×C₃²	—	4	2	no	—
203	C₂²×C₃²	—	4	2	no	—
204	C₂²×C₃²	—	8	2	no	—
205	C₂²×C₃²	#121	1	1	yes	characteristic
206	C₂²×C₃²	#121	1	1	yes	characteristic
207	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
208	C₃²×C₄	—	2	2	no	—
209	C₃²×C₄	—	4	2	no	—
210	C₃²×C₄	#121	1	1	yes	characteristic
211	C₃²×C₄	#121	1	1	yes	characteristic
212	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
213	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
214	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
215	C₂×#41	C₂²×C₃²	1	2	yes	—
216	#137	—	2	2	no	—
217	#137	C₂²×C₃²	1	4	yes	—
218	AGL(1,ℤ/8)	—	2	2	no	—
219	AGL(1,ℤ/8)	C₂²×C₃²	1	4	yes	—
220	#135	—	2	4	no	—
221	#135	—	2	1	no	—
222	#135	—	2	1	no	—
223	#135	—	2	1	no	—
224	#135	—	2	1	no	—
225	C₂×Q₁₆	C₂²×C₃²	1	1	yes	characteristic, complemented
226	C₂×SD₁₆	C₂²×C₃²	1	2	yes	complemented
227	C₂×D₈	C₂²×C₃²	1	1	yes	characteristic, complemented
228	#131	—	2	1	no	—
229	#131	—	2	1	no	—
230	#131	C₂²×C₃²	1	2	yes	—
231	#131	C₂²×C₃²	1	2	yes	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
234	C₂×M₁₆	C₂²×C₃²	1	2	yes	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
237	#108	C₂²×C₃²	1	2	yes	complemented
238	#108	C₂²×C₃²	1	2	yes	complemented
239	#101	C₂²×C₃²	1	4	yes	complemented
240	#100	C₂²×C₃²	1	4	yes	complemented
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	—	2	8	no	—
243	C₂³×C₃	C₃×#41	1	4	yes	—
244	C₃×Q₈	—	2	4	no	—
245	C₃×Q₈	—	2	8	no	—
246	C₃×Q₈	—	2	8	no	—
247	C₃×Q₈	C₂×C₃×D₄	1	8	yes	—
248	C₃×D₄	—	2	8	no	—
249	C₃×D₄	—	2	8	no	—
250	C₃×D₄	—	2	4	no	—
251	C₃×D₄	—	2	8	no	—
252	C₃×D₄	—	2	8	no	—
253	C₃×D₄	—	4	8	no	—
254	C₃×D₄	—	4	8	no	—
255	C₃×D₄	C₂×C₃×D₄	1	8	yes	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	8	no	—
258	C₂×C₃×C₄	—	2	8	no	—
259	C₂×C₃×C₄	—	2	8	no	—
260	C₂×C₃×C₄	—	4	8	no	—
261	C₂×C₃×C₄	—	4	8	no	—
262	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
263	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
264	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
265	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
266	C₂×C₃×C₄	C₃×#41	1	4	yes	—
267	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
268	C₃×C₈	—	2	8	no	—
269	C₃×C₈	—	2	16	no	—
270	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
271	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
272	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
273	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
274	C₂×C₃²	—	2	1	no	—
275	C₂×C₃²	—	2	1	no	—
276	C₂×C₃²	—	2	1	no	—
277	C₂×C₃²	—	4	2	no	—
278	C₂×C₃²	—	8	2	no	—
279	C₂×C₃²	C₂×#121	1	1	yes	characteristic
280	#41	—	2	1	no	—
281	#41	—	2	1	no	—
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	C₃²×D₄	1	2	yes	—
287	#41	C₂³×C₃²	1	2	yes	—
288	C₂×Q₈	C₃²×D₄	1	1	yes	characteristic
289	C₂×Q₈	C₂³×C₃²	1	2	yes	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
293	C₂×D₄	C₂³×C₃²	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
297	Q₁₆	—	2	4	no	—
298	Q₁₆	—	2	1	no	—
299	Q₁₆	—	2	1	no	—
300	SD₁₆	—	2	4	no	—
301	SD₁₆	—	2	4	no	—
302	SD₁₆	—	2	2	no	—
303	SD₁₆	—	2	2	no	—
304	D₈	—	2	4	no	—
305	D₈	—	2	1	no	—
306	D₈	—	2	1	no	—
307	M₁₆	—	2	1	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	C₂³×C₃²	1	2	yes	—
312	M₁₆	C₂³×C₃²	1	4	yes	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
318	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
319	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
320	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
322	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	4	4	no	—
325	C₂²×C₃	—	4	8	no	—
326	C₂²×C₃	—	4	8	no	—
327	C₂²×C₃	—	8	8	no	—
328	C₂²×C₃	C₃×#121	1	4	yes	—
329	C₂²×C₃	C₃×#121	1	4	yes	—
330	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
331	C₃×C₄	—	2	8	no	—
332	C₃×C₄	—	4	8	no	—
333	C₃×C₄	C₃×#121	1	4	yes	—
334	C₃×C₄	C₃×#121	1	4	yes	—
335	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
336	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
337	C₃²	#3067	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₃²×#41	1	1	yes	characteristic
341	Q₈	—	2	1	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	C₂×C₃²×D₄	1	2	yes	—
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	C₂×C₃²×D₄	1	2	yes	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
362	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
363	C₂×C₄	C₃²×#41	1	1	yes	characteristic
364	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	2	4	no	—
367	C₈	C₂×C₃²×D₄	1	1	yes	characteristic
368	C₈	C₂×C₃²×D₄	1	1	yes	characteristic
369	C₈	C₂×C₃²×D₄	1	1	yes	characteristic
370	C₈	C₂×C₃²×D₄	1	1	yes	characteristic
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	2	4	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	—	4	8	no	—
375	C₂×C₃	—	8	8	no	—
376	C₂×C₃	C₂×C₃×#121	1	4	yes	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₃²×#121	1	1	yes	characteristic
383	C₂²	C₃²×#121	1	1	yes	characteristic
384	C₂²	C₂×C₃²×#41	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	C₃²×#121	1	1	yes	characteristic
388	C₄	C₃²×#121	1	1	yes	characteristic
389	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
390	C₄	C₂²×C₃²×D₄	1	1	yes	characteristic
391	C₃	C₃×#3067	1	4	yes	direct product factor
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	4	2	no	—
396	C₂	—	8	2	no	—
397	C₂	C₂×C₃²×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₄	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
socle	C₂×C₃²	C₂×#121
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×#575	C₂	semidirect
2. C₂×C₃²×#135	C₂	semidirect
3. C₂×C₃²×#131	C₂	semidirect
4. C₃²×#473	C₂	semidirect
5. C₃²×#472	C₂	semidirect
6. C₃²×#471	C₂	semidirect
7. C₂×C₃²×#108	C₂	semidirect
8. C₃²×#413	C₂	semidirect
9. C₃×#3067	C₃	direct (N × H)
21. C₂×C₃²×Q₁₆	C₂²	semidirect
22. C₂×C₃²×SD₁₆	C₂²	semidirect
23. C₂×C₃²×D₈	C₂²	semidirect
33. C₃²×#108	C₂²	semidirect
34. C₃²×#108	C₂²	semidirect
35. C₃²×#101	C₂²	semidirect
36. C₃²×#100	C₂²	semidirect
37. C₃×#575	C₂×C₃	semidirect
38. C₂×C₃×#135	C₂×C₃	semidirect
39. C₂×C₃×#131	C₂×C₃	semidirect
40. C₃×#473	C₂×C₃	semidirect
41. C₃×#472	C₂×C₃	semidirect
42. C₃×#471	C₂×C₃	semidirect
43. C₂×C₃×#108	C₂×C₃	semidirect
44. C₃×#413	C₂×C₃	semidirect
88. #3067	C₃²	direct (N × H)
100. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
101. C₂×C₃×SD₁₆	C₂²×C₃	semidirect
102. C₂×C₃×D₈	C₂²×C₃	semidirect
112. C₃×#108	C₂²×C₃	semidirect
113. C₃×#108	C₂²×C₃	semidirect
114. C₃×#101	C₂²×C₃	semidirect
115. C₃×#100	C₂²×C₃	semidirect
149. #575	C₂×C₃²	semidirect
150. C₂×#135	C₂×C₃²	semidirect
151. C₂×#131	C₂×C₃²	semidirect
152. #473	C₂×C₃²	semidirect
153. #472	C₂×C₃²	semidirect
154. #471	C₂×C₃²	semidirect
155. C₂×#108	C₂×C₃²	semidirect
156. #413	C₂×C₃²	semidirect
225. C₂×Q₁₆	C₂²×C₃²	semidirect
226. C₂×SD₁₆	C₂²×C₃²	semidirect
227. C₂×D₈	C₂²×C₃²	semidirect
237. #108	C₂²×C₃²	semidirect
238. #108	C₂²×C₃²	semidirect
239. #101	C₂²×C₃²	semidirect
240. #100	C₂²×C₃²	semidirect
337. C₃²	#3067	direct (N × H)
391. C₃	C₃×#3067	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#575	2
C₂×C₃²×#135	2
C₂×C₃²×#131	2
C₃²×#473	2
C₃²×#472	2
C₃²×#471	2
C₂×C₃²×#108	2
C₃²×#413	2
C₃×#3067	3

Subgroups — C32×#3067 #11770116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3067 #11770116