Subgroups — C₃²×#4807 #13162242

Order 1728.

912 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	C₃²×#946	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#895	C₂	1	1	yes	maximal, characteristic
5	C₃³×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#465	—	3	1	no	maximal
9	C₃×#4807	C₃	1	4	yes	maximal, direct product factor
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃²×D₁₂	—	2	1	no	—
12	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
15	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃²×#215	—	2	2	no	—
17	C₃²×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₃²×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₃²×Dic₃⋊C₄	—	2	1	no	—
21	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₃²×D₃×C₈	—	2	2	no	—
23	C₂×C₃²×SD₁₆	—	3	1	no	—
24	C₂²×C₃²×C₈	—	3	1	no	—
25	C₃²×C₂²⋊Q₈	—	3	1	no	—
26	C₃²×#121	—	3	1	no	—
27	C₃×#946	C₂×C₃	1	4	yes	complemented
28	C₂×C₃×#215	C₂×C₃	1	4	yes	complemented
29	C₂×C₃×D₃×C₈	C₂×C₃	1	4	yes	complemented
30	C₃×#895	C₂×C₃	1	4	yes	—
31	C₃²×#106	—	3	1	no	—
32	C₃²×#103	—	2	4	no	—
33	C₃²×#103	D₃	1	1	yes	characteristic, complemented
34	C₃²×#103	C₂×C₃	1	4	yes	complemented
35	C₃²×#102	—	3	1	no	—
36	C₃×#821	C₂×C₃	1	4	yes	complemented
37	C₃×#808	C₂×C₃	1	4	yes	complemented
38	C₂²×C₃²×D₃	—	2	1	no	—
39	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
40	C₃³×Q₈	—	2	1	no	—
41	C₃³×Q₈	—	2	1	no	—
42	C₂×C₃³×C₄	—	2	1	no	—
43	C₂×C₃³×C₄	—	2	1	no	—
44	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
45	C₂×C₃²×Dic₃	—	2	1	no	—
46	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
47	C₃²×D₁₂	—	2	1	no	—
48	C₃²×D₁₂	—	2	1	no	—
49	C₃²×D₁₂	—	4	2	no	—
50	C₃²×C₄×D₃	—	2	1	no	—
51	C₃²×C₄×D₃	—	2	1	no	—
52	C₃³×C₈	—	2	1	no	—
53	C₃²×C₃⋊C₈	D₄	1	2	yes	complemented
54	C₃×#465	—	3	4	no	—
55	#4807	C₃²	1	1	yes	characteristic, direct product factor
56	C₂×C₃²×Q₈	—	2	4	no	—
57	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
58	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
59	C₂×C₃²×D₄	—	3	1	no	—
60	C₂×C₃²×D₄	—	6	1	no	—
61	C₂²×C₃²×C₄	—	3	1	no	—
62	C₂×C₃×D₁₂	—	2	4	no	—
63	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
64	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
65	C₃²×SD₁₆	—	6	2	no	—
66	C₂×C₃²×C₈	—	2	4	no	—
67	C₂×C₃²×C₈	—	3	1	no	—
68	C₂×C₃²×C₈	—	6	2	no	—
69	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
71	C₃²×C₄⋊C₄	—	2	4	no	—
72	C₃²×C₄⋊C₄	—	3	1	no	—
73	C₃²×C₄⋊C₄	—	6	1	no	—
74	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
75	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
76	C₃²×C₂²⋊C₄	—	6	1	no	—
77	C₃²×C₂²⋊C₄	—	6	1	no	—
78	C₃×#215	—	2	8	no	—
79	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
80	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
81	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
82	C₃×Dic₃⋊C₄	—	2	4	no	—
83	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
84	C₃×D₃×C₈	—	2	8	no	—
85	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃²×D₃	—	2	1	no	—
87	C₂×C₃²×D₃	—	2	1	no	—
88	C₂×C₃²×D₃	—	4	1	no	—
89	C₂×C₃²×D₃	—	4	1	no	—
90	C₂×C₃²×D₃	—	4	1	no	—
91	C₂×C₃²×D₃	SD₁₆	1	2	yes	complemented
92	C₃³×C₄	—	4	1	no	—
93	C₃³×C₄	—	4	1	no	—
94	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
95	C₃³×C₄	#41	1	1	yes	characteristic
96	C₃²×Dic₃	—	2	1	no	—
97	C₃²×Dic₃	—	4	1	no	—
98	C₂×C₃×SD₁₆	—	3	4	no	—
99	C₂²×C₃×C₈	—	3	4	no	—
100	C₃×C₂²⋊Q₈	—	3	4	no	—
101	C₃×#121	—	3	4	no	—
102	#946	C₂×C₃²	1	1	yes	characteristic, complemented
103	C₂×#215	C₂×C₃²	1	1	yes	characteristic, complemented
104	C₂×D₃×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
105	#895	C₂×C₃²	1	1	yes	characteristic
106	C₃×#106	—	3	4	no	—
107	C₃×#103	—	2	4	no	—
108	C₃×#103	C₃×D₃	1	4	yes	complemented
109	C₃×#103	C₂×C₃²	1	1	yes	characteristic, complemented
110	C₃×#102	—	3	4	no	—
111	#821	C₂×C₃²	1	1	yes	characteristic, complemented
112	#808	C₂×C₃²	1	1	yes	characteristic, complemented
113	C₂³×C₃²	—	3	1	no	—
114	C₂³×C₃²	—	6	1	no	—
115	C₂²×C₃×D₃	—	2	4	no	—
116	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
117	C₃²×Q₈	—	2	8	no	—
118	C₃²×Q₈	—	2	1	no	—
119	C₃²×Q₈	—	2	1	no	—
120	C₃²×Q₈	—	2	4	no	—
121	C₃²×Q₈	—	2	4	no	—
122	C₃²×Q₈	—	4	4	no	—
123	C₃²×D₄	—	6	1	no	—
124	C₃²×D₄	—	6	1	no	—
125	C₃²×D₄	—	12	2	no	—
126	C₂×C₃²×C₄	—	2	1	no	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	4	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	3	1	no	—
132	C₂×C₃²×C₄	—	4	4	no	—
133	C₂×C₃²×C₄	—	4	4	no	—
134	C₂×C₃²×C₄	—	6	1	no	—
135	C₂×C₃²×C₄	—	6	1	no	—
136	C₂×C₃²×C₄	—	6	1	no	—
137	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
139	C₂×C₃×Dic₃	—	2	4	no	—
140	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
141	C₃×D₁₂	—	2	4	no	—
142	C₃×D₁₂	—	2	4	no	—
143	C₃×D₁₂	—	4	8	no	—
144	C₃×C₄×D₃	—	2	4	no	—
145	C₃×C₄×D₃	—	2	4	no	—
146	C₃²×C₈	—	2	1	no	—
147	C₃²×C₈	—	2	4	no	—
148	C₃²×C₈	—	3	2	no	—
149	C₃²×C₈	—	4	4	no	—
150	C₃×C₃⋊C₈	C₃×D₄	1	8	yes	complemented
151	#465	—	3	1	no	Sylow
152	C₂×C₃³	#121	1	1	yes	characteristic
153	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₃³	#135	1	1	yes	characteristic
155	C₃²×D₃	—	2	2	no	—
156	C₃²×D₃	—	8	1	no	—
157	C₂×C₃×Q₈	—	2	4	no	—
158	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
159	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
160	C₂×C₃×D₄	—	3	4	no	—
161	C₂×C₃×D₄	—	6	4	no	—
162	C₂²×C₃×C₄	—	3	4	no	—
163	C₂×D₁₂	—	2	1	no	—
164	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
166	C₃×SD₁₆	—	6	8	no	—
167	C₂×C₃×C₈	—	2	4	no	—
168	C₂×C₃×C₈	—	3	4	no	—
169	C₂×C₃×C₈	—	6	8	no	—
170	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
171	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	3	4	no	—
174	C₃×C₄⋊C₄	—	6	4	no	—
175	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
176	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
177	C₃×C₂²⋊C₄	—	6	4	no	—
178	C₃×C₂²⋊C₄	—	6	4	no	—
179	#215	—	2	2	no	—
180	(C₂×D₃)⋊C₄	—	2	1	no	—
181	(C₂×D₃)⋊C₄	—	2	1	no	—
182	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
183	Dic₃⋊C₄	—	2	1	no	—
184	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
185	D₃×C₈	—	2	2	no	—
186	C₂²×C₃²	—	2	4	no	—
187	C₂²×C₃²	—	3	2	no	—
188	C₂²×C₃²	—	6	1	no	—
189	C₂²×C₃²	—	6	1	no	—
190	C₂²×C₃²	—	12	1	no	—
191	C₂²×C₃²	—	12	1	no	—
192	C₂²×C₃²	—	12	1	no	—
193	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
194	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
195	C₂×C₃×D₃	—	2	4	no	—
196	C₂×C₃×D₃	—	2	4	no	—
197	C₂×C₃×D₃	—	4	4	no	—
198	C₂×C₃×D₃	—	4	4	no	—
199	C₂×C₃×D₃	—	4	4	no	—
200	C₂×C₃×D₃	C₃×SD₁₆	1	8	yes	complemented
201	C₃²×C₄	—	2	4	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	4	8	no	—
204	C₃²×C₄	—	4	1	no	—
205	C₃²×C₄	—	4	1	no	—
206	C₃²×C₄	—	4	4	no	—
207	C₃²×C₄	—	4	4	no	—
208	C₃²×C₄	—	6	1	no	—
209	C₃²×C₄	—	8	4	no	—
210	C₃²×C₄	—	12	1	no	—
211	C₃²×C₄	#235	1	1	yes	characteristic
212	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
213	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
214	C₃²×C₄	C₃×#41	1	4	yes	—
215	C₃×Dic₃	—	2	4	no	—
216	C₃×Dic₃	—	4	4	no	—
217	C₂×SD₁₆	—	3	1	no	—
218	C₂²×C₈	—	3	1	no	—
219	C₂²⋊Q₈	—	3	1	no	—
220	#121	—	3	1	no	—
221	#106	—	3	1	no	—
222	#103	C₃²×D₃	1	1	yes	characteristic, complemented
223	#102	—	3	1	no	—
224	C₃³	#465	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₃	—	3	4	no	—
226	C₂³×C₃	—	6	4	no	—
227	C₂²×D₃	—	2	1	no	—
228	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
229	C₃×Q₈	—	2	8	no	—
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	2	4	no	—
232	C₃×Q₈	—	2	1	no	—
233	C₃×Q₈	—	2	1	no	—
234	C₃×Q₈	—	4	4	no	—
235	C₃×D₄	—	6	4	no	—
236	C₃×D₄	—	6	4	no	—
237	C₃×D₄	—	12	8	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	3	4	no	—
244	C₂×C₃×C₄	—	4	4	no	—
245	C₂×C₃×C₄	—	4	4	no	—
246	C₂×C₃×C₄	—	6	4	no	—
247	C₂×C₃×C₄	—	6	4	no	—
248	C₂×C₃×C₄	—	6	4	no	—
249	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
250	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
251	C₂×Dic₃	—	2	1	no	—
252	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
253	D₁₂	—	2	1	no	—
254	D₁₂	—	2	1	no	—
255	D₁₂	—	4	2	no	—
256	C₄×D₃	—	2	1	no	—
257	C₄×D₃	—	2	1	no	—
258	C₃×C₈	—	2	4	no	—
259	C₃×C₈	—	2	1	no	—
260	C₃×C₈	—	3	8	no	—
261	C₃×C₈	—	4	4	no	—
262	C₃⋊C₈	C₃²×D₄	1	2	yes	complemented
263	C₂×C₃²	—	2	4	no	—
264	C₂×C₃²	—	2	4	no	—
265	C₂×C₃²	—	2	4	no	—
266	C₂×C₃²	—	6	2	no	—
267	C₂×C₃²	—	24	1	no	—
268	C₂×C₃²	#884	1	1	yes	characteristic
269	C₂×C₃²	D₃×SD₁₆	1	1	yes	characteristic
270	C₂×C₃²	#919	1	1	yes	characteristic
271	C₂×C₃²	C₃×#121	1	4	yes	—
272	C₂×C₃²	C₂×C₃×SD₁₆	1	4	yes	—
273	C₂×C₃²	C₃×#135	1	4	yes	—
274	C₃×D₃	—	2	8	no	—
275	C₃×D₃	—	8	4	no	—
276	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
277	C₂×D₄	—	3	1	no	—
278	C₂×D₄	—	6	1	no	—
279	C₂²×C₄	—	3	1	no	—
280	SD₁₆	—	6	2	no	—
281	C₂×C₈	—	3	1	no	—
282	C₂×C₈	—	6	2	no	—
283	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
284	C₄⋊C₄	—	3	1	no	—
285	C₄⋊C₄	—	6	1	no	—
286	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
287	C₂²⋊C₄	—	6	1	no	—
288	C₂²⋊C₄	—	6	1	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	3	8	no	—
291	C₂²×C₃	—	6	4	no	—
292	C₂²×C₃	—	6	4	no	—
293	C₂²×C₃	—	12	4	no	—
294	C₂²×C₃	—	12	4	no	—
295	C₂²×C₃	—	12	4	no	—
296	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
297	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
298	C₂×D₃	—	2	1	no	—
299	C₂×D₃	—	2	1	no	—
300	C₂×D₃	—	4	1	no	—
301	C₂×D₃	—	4	1	no	—
302	C₂×D₃	—	4	1	no	—
303	C₂×D₃	C₃²×SD₁₆	1	2	yes	complemented
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	4	8	no	—
307	C₃×C₄	—	4	4	no	—
308	C₃×C₄	—	4	4	no	—
309	C₃×C₄	—	4	1	no	—
310	C₃×C₄	—	4	1	no	—
311	C₃×C₄	—	6	4	no	—
312	C₃×C₄	—	8	4	no	—
313	C₃×C₄	—	12	4	no	—
314	C₃×C₄	C₃×#235	1	4	yes	—
315	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
316	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
317	C₃×C₄	C₃²×#41	1	1	yes	characteristic
318	Dic₃	—	2	1	no	—
319	Dic₃	—	4	1	no	—
320	C₃²	—	2	4	no	—
321	C₃²	#4807	1	1	yes	characteristic, direct product factor
322	C₃²	C₃×#465	1	4	yes	complemented
323	C₂³	—	3	1	no	—
324	C₂³	—	6	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	D₄	—	6	1	no	—
328	D₄	—	6	1	no	—
329	D₄	—	12	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	3	1	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	1	no	—
335	C₂×C₄	—	6	1	no	—
336	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	3	2	no	—
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	2	4	no	—
341	C₂×C₃	—	2	4	no	—
342	C₂×C₃	—	6	8	no	—
343	C₂×C₃	—	24	4	no	—
344	C₂×C₃	C₃×#884	1	4	yes	—
345	C₂×C₃	C₃×D₃×SD₁₆	1	4	yes	—
346	C₂×C₃	C₃×#919	1	4	yes	—
347	C₂×C₃	C₃²×#121	1	1	yes	characteristic
348	C₂×C₃	C₂×C₃²×SD₁₆	1	1	yes	characteristic
349	C₂×C₃	C₃²×#135	1	1	yes	characteristic
350	D₃	—	2	2	no	—
351	D₃	—	8	1	no	—
352	C₂²	—	3	2	no	—
353	C₂²	—	6	1	no	—
354	C₂²	—	6	1	no	—
355	C₂²	—	12	1	no	—
356	C₂²	—	12	1	no	—
357	C₂²	—	12	1	no	—
358	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	6	1	no	—
362	C₄	—	12	1	no	—
363	C₄	C₃²×#235	1	1	yes	characteristic
364	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
365	C₃	—	2	4	no	—
366	C₃	C₃×#4807	1	4	yes	direct product factor
367	C₃	C₃²×#465	1	1	yes	characteristic, complemented
368	C₂	—	6	2	no	—
369	C₂	—	24	1	no	—
370	C₂	C₃²×#884	1	1	yes	characteristic
371	C₂	C₃²×D₃×SD₁₆	1	1	yes	characteristic
372	C₂	C₃²×#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³×C₃²
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₃³×#103	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₃²×#895	C₂
hypercenter	C₃²×#103	D₃
hypocenter	C₃	C₃²×#465
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₃²×#103

Complements

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

N	H ≅ G/N	type
1. C₃²×#946	C₂	semidirect
2. C₂×C₃²×#215	C₂	semidirect
3. C₂×C₃²×D₃×C₈	C₂	semidirect
5. C₃³×#103	C₂	semidirect
6. C₃²×#821	C₂	semidirect
7. C₃²×#808	C₂	semidirect
9. C₃×#4807	C₃	direct (N × H)
27. C₃×#946	C₂×C₃	semidirect
28. C₂×C₃×#215	C₂×C₃	semidirect
29. C₂×C₃×D₃×C₈	C₂×C₃	semidirect
33. C₃²×#103	D₃	semidirect
34. C₃²×#103	C₂×C₃	semidirect
36. C₃×#821	C₂×C₃	semidirect
37. C₃×#808	C₂×C₃	semidirect
53. C₃²×C₃⋊C₈	D₄	semidirect
55. #4807	C₃²	direct (N × H)
91. C₂×C₃²×D₃	SD₁₆	semidirect
102. #946	C₂×C₃²	semidirect
103. C₂×#215	C₂×C₃²	semidirect
104. C₂×D₃×C₈	C₂×C₃²	semidirect
108. C₃×#103	C₃×D₃	semidirect
109. C₃×#103	C₂×C₃²	semidirect
111. #821	C₂×C₃²	semidirect
112. #808	C₂×C₃²	semidirect
150. C₃×C₃⋊C₈	C₃×D₄	semidirect
200. C₂×C₃×D₃	C₃×SD₁₆	semidirect
222. #103	C₃²×D₃	semidirect
224. C₃³	#465	semidirect
262. C₃⋊C₈	C₃²×D₄	semidirect
303. C₂×D₃	C₃²×SD₁₆	semidirect
321. C₃²	#4807	direct (N × H)
322. C₃²	C₃×#465	semidirect
366. C₃	C₃×#4807	direct (N × H)
367. C₃	C₃²×#465	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#946	2
C₂×C₃²×#215	2
C₂×C₃²×D₃×C₈	2
C₃²×#895	2
C₃³×#103	2
C₃²×#821	2
C₃²×#808	2
C₃²×#465	3
C₃×#4807	3

Subgroups — C32×#4807 #13162242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#4807 #13162242