Subgroups — C₃²×#5585 #13178962

Order 1728.

1696 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#947	C₂	1	2	yes	maximal, complemented
3	C₃²×#894	C₂	1	4	yes	maximal, complemented
4	C₃²×#893	C₂	1	2	yes	maximal, complemented
5	C₃²×#875	C₂	1	2	yes	maximal, complemented
6	C₃²×#874	C₂	1	1	yes	maximal, characteristic
7	C₃²×C₄×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₃²×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#559	—	3	1	no	maximal
10	C₃×#5585	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
13	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
14	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
15	C₂×C₃²×C₄×D₃	C₂²	1	4	yes	—
16	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃³×C₄²	C₂²	1	1	yes	characteristic
20	C₃³×C₄²	C₂²	1	2	yes	—
21	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
26	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
27	C₃²×#127	—	3	1	no	—
28	C₃²×#124	—	3	2	no	—
29	C₃²×#124	—	3	2	no	—
30	C₃²×#123	—	3	4	no	—
31	C₃²×C₄×Q₈	—	2	4	no	—
32	C₃²×C₄×Q₈	—	3	1	no	—
33	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic, complemented
34	C₃²×C₄×Q₈	C₂×C₃	1	4	yes	complemented
35	C₃²×C₄×D₄	—	3	2	no	—
36	C₃²×C₄×D₄	—	3	2	no	—
37	C₃×#947	C₂×C₃	1	8	yes	complemented
38	C₃×#894	C₂×C₃	1	16	yes	complemented
39	C₃×#893	C₂×C₃	1	8	yes	complemented
40	C₃×#875	C₂×C₃	1	8	yes	complemented
41	C₃×#874	C₂×C₃	1	4	yes	—
42	C₃×C₄×D₁₂	C₂×C₃	1	8	yes	complemented
43	C₃×C₄×Dic₆	C₂×C₃	1	4	yes	complemented
44	C₂²×C₃²×D₃	C₂³	1	4	yes	—
45	C₃³×Q₈	—	2	2	no	—
46	C₂×C₃³×C₄	C₂³	1	2	yes	—
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₂×C₃³×C₄	C₂³	1	2	yes	—
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
52	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
53	C₃²×D₁₂	—	2	4	no	—
54	C₃²×D₁₂	—	2	4	no	—
55	C₃²×D₁₂	—	4	2	no	—
56	C₃²×C₄×D₃	—	4	4	no	—
57	C₃²×Dic₆	—	2	2	no	—
58	C₃×#559	—	3	4	no	—
59	#5585	C₃²	1	1	yes	characteristic, direct product factor
60	C₂×C₃²×Q₈	—	2	4	no	—
61	C₂×C₃²×Q₈	—	3	1	no	—
62	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
64	C₂×C₃²×D₄	—	3	2	no	—
65	C₂×C₃²×D₄	—	3	2	no	—
66	C₂×C₃²×D₄	—	3	2	no	—
67	C₂²×C₃²×C₄	—	3	4	no	—
68	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
69	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
70	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
71	C₂×C₃×C₄×D₃	C₂²×C₃	1	16	yes	—
72	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
73	C₃²×C₄⋊C₄	—	2	4	no	—
74	C₃²×C₄⋊C₄	—	2	8	no	—
75	C₃²×C₄⋊C₄	—	3	1	no	—
76	C₃²×C₄⋊C₄	—	3	2	no	—
77	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
79	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
80	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
81	C₃²×C₂²⋊C₄	—	3	4	no	—
82	C₃²×C₂²⋊C₄	—	3	4	no	—
83	C₃²×C₂²⋊C₄	—	3	4	no	—
84	C₃²×C₄²	—	2	8	no	—
85	C₃²×C₄²	—	2	4	no	—
86	C₃²×C₄²	—	3	2	no	—
87	C₃²×C₄²	C₂×D₃	1	2	yes	—
88	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
89	C₃²×C₄²	C₂²×C₃	1	4	yes	—
90	C₃²×C₄²	C₂²×C₃	1	8	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	—
93	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	—
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
96	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
97	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
98	C₂×C₃²×D₃	—	2	4	no	—
99	C₂×C₃²×D₃	—	2	4	no	—
100	C₂×C₃²×D₃	—	2	4	no	—
101	C₃³×C₄	—	2	2	no	—
102	C₃³×C₄	—	2	2	no	—
103	C₃³×C₄	—	2	1	no	—
104	C₃³×C₄	#41	1	2	yes	—
105	C₃³×C₄	#41	1	2	yes	—
106	C₃²×Dic₃	—	2	2	no	—
107	C₃²×Dic₃	—	2	2	no	—
108	C₃×#127	—	3	4	no	—
109	C₃×#124	—	3	8	no	—
110	C₃×#124	—	3	8	no	—
111	C₃×#123	—	3	16	no	—
112	C₃×C₄×Q₈	—	2	4	no	—
113	C₃×C₄×Q₈	—	3	4	no	—
114	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
115	C₃×C₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
116	C₃×C₄×D₄	—	3	8	no	—
117	C₃×C₄×D₄	—	3	8	no	—
118	#947	C₂×C₃²	1	2	yes	complemented
119	#894	C₂×C₃²	1	4	yes	complemented
120	#893	C₂×C₃²	1	2	yes	complemented
121	#875	C₂×C₃²	1	2	yes	complemented
122	#874	C₂×C₃²	1	1	yes	characteristic
123	C₄×D₁₂	C₂×C₃²	1	2	yes	complemented
124	C₄×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
125	C₂³×C₃²	—	3	4	no	—
126	C₂²×C₃×D₃	C₂³×C₃	1	16	yes	—
127	C₃²×Q₈	—	2	16	no	—
128	C₃²×Q₈	—	2	2	no	—
129	C₃²×Q₈	—	2	8	no	—
130	C₃²×Q₈	—	6	2	no	—
131	C₃²×D₄	—	6	4	no	—
132	C₃²×D₄	—	6	4	no	—
133	C₃²×D₄	—	12	2	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	—	2	8	no	—
136	C₂×C₃²×C₄	—	2	4	no	—
137	C₂×C₃²×C₄	—	2	8	no	—
138	C₂×C₃²×C₄	—	2	4	no	—
139	C₂×C₃²×C₄	—	3	2	no	—
140	C₂×C₃²×C₄	—	3	2	no	—
141	C₂×C₃²×C₄	—	12	4	no	—
142	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
143	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
148	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
151	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
152	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
153	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
154	C₃×D₁₂	—	2	16	no	—
155	C₃×D₁₂	—	2	16	no	—
156	C₃×D₁₂	—	4	8	no	—
157	C₃×C₄×D₃	—	4	16	no	—
158	C₃×Dic₆	—	2	8	no	—
159	#559	—	3	1	no	Sylow
160	C₂×C₃³	C₂×#41	1	1	yes	characteristic
161	C₂×C₃³	C₂×#41	1	1	yes	characteristic
162	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
163	C₃²×D₃	—	4	4	no	—
164	C₂×C₃×Q₈	—	2	4	no	—
165	C₂×C₃×Q₈	—	3	4	no	—
166	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
167	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
168	C₂×C₃×D₄	—	3	8	no	—
169	C₂×C₃×D₄	—	3	8	no	—
170	C₂×C₃×D₄	—	3	8	no	—
171	C₂²×C₃×C₄	—	3	16	no	—
172	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
173	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
174	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
175	C₂×C₄×D₃	C₂²×C₃²	1	4	yes	—
176	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
177	C₃×C₄⋊C₄	—	2	4	no	—
178	C₃×C₄⋊C₄	—	2	8	no	—
179	C₃×C₄⋊C₄	—	3	8	no	—
180	C₃×C₄⋊C₄	—	3	4	no	—
181	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
182	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
183	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
185	C₃×C₂²⋊C₄	—	3	16	no	—
186	C₃×C₂²⋊C₄	—	3	16	no	—
187	C₃×C₂²⋊C₄	—	3	16	no	—
188	C₃×C₄²	—	2	8	no	—
189	C₃×C₄²	—	2	4	no	—
190	C₃×C₄²	—	3	8	no	—
191	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
192	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
193	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
194	C₃×C₄²	C₂²×C₃²	1	2	yes	—
195	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	—
196	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	—
197	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	—
198	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
199	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
200	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
201	C₂²×C₃²	—	2	4	no	—
202	C₂²×C₃²	—	6	4	no	—
203	C₂²×C₃²	—	6	4	no	—
204	C₂²×C₃²	—	6	4	no	—
205	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
206	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
207	C₂×C₃×D₃	—	2	16	no	—
208	C₂×C₃×D₃	—	2	16	no	—
209	C₂×C₃×D₃	—	2	16	no	—
210	C₃²×C₄	—	2	16	no	—
211	C₃²×C₄	—	2	2	no	—
212	C₃²×C₄	—	2	2	no	—
213	C₃²×C₄	—	2	1	no	—
214	C₃²×C₄	—	2	8	no	—
215	C₃²×C₄	—	2	8	no	—
216	C₃²×C₄	—	2	8	no	—
217	C₃²×C₄	—	2	8	no	—
218	C₃²×C₄	—	2	4	no	—
219	C₃²×C₄	—	4	8	no	—
220	C₃²×C₄	—	4	4	no	—
221	C₃²×C₄	—	6	2	no	—
222	C₃²×C₄	—	6	2	no	—
223	C₃²×C₄	#235	1	2	yes	—
224	C₃²×C₄	#239	1	2	yes	—
225	C₃²×C₄	C₃×#41	1	8	yes	—
226	C₃²×C₄	C₃×#41	1	8	yes	—
227	C₃×Dic₃	—	2	8	no	—
228	C₃×Dic₃	—	2	8	no	—
229	#127	—	3	1	no	—
230	#124	—	3	2	no	—
231	#124	—	3	2	no	—
232	#123	—	3	4	no	—
233	C₄×Q₈	—	3	1	no	—
234	C₄×Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
235	C₄×D₄	—	3	2	no	—
236	C₄×D₄	—	3	2	no	—
237	C₃³	#559	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	3	16	no	—
239	C₂²×D₃	C₂³×C₃²	1	4	yes	—
240	C₃×Q₈	—	2	16	no	—
241	C₃×Q₈	—	2	8	no	—
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	6	8	no	—
244	C₃×D₄	—	6	16	no	—
245	C₃×D₄	—	6	16	no	—
246	C₃×D₄	—	12	8	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	8	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	3	8	no	—
253	C₂×C₃×C₄	—	3	8	no	—
254	C₂×C₃×C₄	—	12	16	no	—
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
256	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
257	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
258	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
260	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
262	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
263	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
265	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
266	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
267	D₁₂	—	2	4	no	—
268	D₁₂	—	2	4	no	—
269	D₁₂	—	4	2	no	—
270	C₄×D₃	—	4	4	no	—
271	Dic₆	—	2	2	no	—
272	C₂×C₃²	—	2	4	no	—
273	C₂×C₃²	—	2	4	no	—
274	C₂×C₃²	—	2	4	no	—
275	C₂×C₃²	—	12	4	no	—
276	C₂×C₃²	C₂×#235	1	1	yes	characteristic
277	C₂×C₃²	C₂×#239	1	1	yes	characteristic
278	C₂×C₃²	#1009	1	1	yes	characteristic
279	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
280	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
281	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
282	C₃×D₃	—	4	16	no	—
283	C₂×Q₈	—	3	1	no	—
284	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
285	C₂×D₄	—	3	2	no	—
286	C₂×D₄	—	3	2	no	—
287	C₂×D₄	—	3	2	no	—
288	C₂²×C₄	—	3	4	no	—
289	C₄⋊C₄	—	3	1	no	—
290	C₄⋊C₄	—	3	2	no	—
291	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
292	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
293	C₂²⋊C₄	—	3	4	no	—
294	C₂²⋊C₄	—	3	4	no	—
295	C₂²⋊C₄	—	3	4	no	—
296	C₄²	—	3	2	no	—
297	C₄²	C₂×C₃²×D₃	1	2	yes	—
298	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
299	C₂²×C₃	—	2	4	no	—
300	C₂²×C₃	—	6	16	no	—
301	C₂²×C₃	—	6	16	no	—
302	C₂²×C₃	—	6	16	no	—
303	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
304	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
305	C₂×D₃	—	2	4	no	—
306	C₂×D₃	—	2	4	no	—
307	C₂×D₃	—	2	4	no	—
308	C₃×C₄	—	2	16	no	—
309	C₃×C₄	—	2	8	no	—
310	C₃×C₄	—	2	8	no	—
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	8	no	—
316	C₃×C₄	—	2	8	no	—
317	C₃×C₄	—	4	8	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	—	6	8	no	—
320	C₃×C₄	—	6	8	no	—
321	C₃×C₄	C₃×#235	1	8	yes	—
322	C₃×C₄	C₃×#239	1	8	yes	—
323	C₃×C₄	C₃²×#41	1	2	yes	—
324	C₃×C₄	C₃²×#41	1	2	yes	—
325	Dic₃	—	2	2	no	—
326	Dic₃	—	2	2	no	—
327	C₃²	—	2	4	no	—
328	C₃²	#5585	1	1	yes	characteristic, direct product factor
329	C₃²	C₃×#559	1	4	yes	complemented
330	C₂³	—	3	4	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	6	2	no	—
333	D₄	—	6	4	no	—
334	D₄	—	6	4	no	—
335	D₄	—	12	2	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	3	2	no	—
338	C₂×C₄	—	12	4	no	—
339	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
340	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
341	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
344	C₂×C₃	—	2	4	no	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	—	2	4	no	—
347	C₂×C₃	—	12	16	no	—
348	C₂×C₃	C₂×C₃×#235	1	4	yes	—
349	C₂×C₃	C₂×C₃×#239	1	4	yes	—
350	C₂×C₃	C₃×#1009	1	4	yes	—
351	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
352	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
353	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
354	D₃	—	4	4	no	—
355	C₂²	—	6	4	no	—
356	C₂²	—	6	4	no	—
357	C₂²	—	6	4	no	—
358	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	1	no	—
362	C₄	—	6	2	no	—
363	C₄	—	6	2	no	—
364	C₄	C₃²×#235	1	2	yes	—
365	C₄	C₃²×#239	1	2	yes	—
366	C₃	—	2	4	no	—
367	C₃	C₃×#5585	1	4	yes	direct product factor
368	C₃	C₃²×#559	1	1	yes	characteristic, complemented
369	C₂	—	12	4	no	—
370	C₂	C₂×C₃²×#235	1	1	yes	characteristic
371	C₂	C₂×C₃²×#239	1	1	yes	characteristic
372	C₂	C₃²×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃²×#874	C₂
hypercenter	C₃²×C₄×Q₈	D₃
hypocenter	C₃	C₃²×#559
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
2. C₃²×#947	C₂	semidirect
3. C₃²×#894	C₂	semidirect
4. C₃²×#893	C₂	semidirect
5. C₃²×#875	C₂	semidirect
7. C₃²×C₄×D₁₂	C₂	semidirect
8. C₃²×C₄×Dic₆	C₂	semidirect
10. C₃×#5585	C₃	direct (N × H)
33. C₃²×C₄×Q₈	D₃	semidirect
34. C₃²×C₄×Q₈	C₂×C₃	semidirect
37. C₃×#947	C₂×C₃	semidirect
38. C₃×#894	C₂×C₃	semidirect
39. C₃×#893	C₂×C₃	semidirect
40. C₃×#875	C₂×C₃	semidirect
42. C₃×C₄×D₁₂	C₂×C₃	semidirect
43. C₃×C₄×Dic₆	C₂×C₃	semidirect
59. #5585	C₃²	direct (N × H)
114. C₃×C₄×Q₈	C₃×D₃	semidirect
115. C₃×C₄×Q₈	C₂×C₃²	semidirect
118. #947	C₂×C₃²	semidirect
119. #894	C₂×C₃²	semidirect
120. #893	C₂×C₃²	semidirect
121. #875	C₂×C₃²	semidirect
123. C₄×D₁₂	C₂×C₃²	semidirect
124. C₄×Dic₆	C₂×C₃²	semidirect
234. C₄×Q₈	C₃²×D₃	semidirect
237. C₃³	#559	semidirect
328. C₃²	#5585	direct (N × H)
329. C₃²	C₃×#559	semidirect
367. C₃	C₃×#5585	direct (N × H)
368. C₃	C₃²×#559	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₄×Q₈	2
C₃²×#947	2
C₃²×#894	2
C₃²×#893	2
C₃²×#875	2
C₃²×#874	2
C₃²×C₄×D₁₂	2
C₃²×C₄×Dic₆	2
C₃²×#559	3
C₃×#5585	3

Subgroups — C32×#5585 #13178962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5585 #13178962