Subgroups — C₃×#90320 #13060975

Order 1344.

588 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1157	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6459	C₂	1	2	yes	maximal, complemented
7	C₃×#6458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6458	C₂	1	2	yes	maximal, complemented
9	C₃×D₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6447	C₂	1	2	yes	maximal, complemented
11	C₃×#6447	C₂	1	2	yes	maximal, complemented
12	#90320	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	—
18	C₃×#1161	—	2	4	no	—
19	C₃×#1157	—	2	4	no	—
20	C₂×C₃×D₂₈	C₂²	1	2	yes	—
21	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₂₈	C₂²	1	2	yes	—
24	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
25	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
28	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic
29	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	—
31	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
35	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic
36	C₃×Dic₇⋊C₄	C₂²	1	2	yes	—
37	C₃×Dic₇⋊C₄	C₂²	1	2	yes	—
38	C₂×#1161	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#1157	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
41	#6509	C₂×C₃	1	1	yes	characteristic, complemented
42	#6493	C₂×C₃	1	1	yes	characteristic, complemented
43	#6459	C₂×C₃	1	2	yes	complemented
44	#6458	C₂×C₃	1	1	yes	characteristic, complemented
45	#6458	C₂×C₃	1	2	yes	complemented
46	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
47	#6447	C₂×C₃	1	2	yes	complemented
48	#6447	C₂×C₃	1	2	yes	complemented
49	C₃×#537	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
51	C₂²×C₃×D₇	C₂³	1	2	yes	—
52	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
53	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
54	C₃×C₇×Q₈	—	2	2	no	—
55	C₂×C₃×C₄×C₇	—	2	2	no	—
56	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₃×C₂²⋊D₇	—	2	2	no	—
61	C₃×C₂²⋊D₇	—	2	2	no	—
62	C₃×C₂²⋊D₇	—	4	2	no	—
63	C₂×C₃×Dic₇	C₂³	1	2	yes	—
64	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
65	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
66	C₃×D₂₈	—	2	2	no	—
67	C₃×D₂₈	—	2	4	no	—
68	C₃×D₂₈	—	2	2	no	—
69	C₃×D₂₈	—	4	2	no	—
70	C₃×C₄×D₇	—	2	2	no	—
71	C₃×C₄×D₇	—	2	4	no	—
72	C₃×C₄×D₇	—	4	2	no	—
73	C₃×C₄×D₇	D₄	1	4	yes	complemented
74	C₃×Dic₁₄	—	2	2	no	—
75	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	—
80	#1161	—	2	4	no	—
81	#1157	—	2	4	no	—
82	C₂×D₂₈	C₂²×C₃	1	2	yes	—
83	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
85	C₂×D₂₈	C₂²×C₃	1	2	yes	—
86	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
87	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
89	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
90	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic
91	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
96	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
97	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
98	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
99	Dic₇⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×#41	—	7	1	no	—
101	C₂×C₃×#41	—	7	1	no	—
102	C₃×C₂²⋊Q₈	—	7	1	no	—
103	C₃×C₂²⋊Q₈	—	7	2	no	—
104	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, complemented
105	C₃×#121	—	7	1	no	—
106	C₃×#121	—	7	1	no	—
107	C₃×#121	—	7	2	no	—
108	C₃×#121	—	7	2	no	—
109	C₃×#121	—	7	2	no	—
110	C₂×C₃×C₄⋊C₄	—	7	1	no	—
111	C₂²×C₃×C₇	—	2	1	no	—
112	C₂²×C₃×C₇	—	2	1	no	—
113	C₂²×C₃×C₇	—	2	1	no	—
114	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
115	C₂×C₃×D₇	—	2	1	no	—
116	C₂×C₃×D₇	—	2	1	no	—
117	C₂×C₃×D₇	—	2	2	no	—
118	C₂×C₃×D₇	—	2	1	no	—
119	C₂×C₃×D₇	—	2	1	no	—
120	C₂×C₃×D₇	—	2	2	no	—
121	C₂×C₃×D₇	—	2	2	no	—
122	C₂×C₃×D₇	—	2	1	no	—
123	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
124	C₃×C₄×C₇	—	2	1	no	—
125	C₃×C₄×C₇	—	2	2	no	—
126	C₃×C₄×C₇	—	2	2	no	—
127	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
128	C₃×Dic₇	—	2	1	no	—
129	C₃×Dic₇	—	2	2	no	—
130	C₃×Dic₇	C₂×D₄	1	2	yes	—
131	#537	—	7	1	no	Sylow
132	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
133	C₂²×D₇	C₂³×C₃	1	2	yes	—
134	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
135	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
136	C₇×Q₈	—	2	2	no	—
137	C₂×C₄×C₇	—	2	2	no	—
138	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
139	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
140	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
141	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
142	C₂²⋊D₇	—	2	2	no	—
143	C₂²⋊D₇	—	2	2	no	—
144	C₂²⋊D₇	—	4	2	no	—
145	C₂×Dic₇	C₂³×C₃	1	2	yes	—
146	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
147	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
148	D₂₈	—	2	2	no	—
149	D₂₈	—	2	4	no	—
150	D₂₈	—	2	2	no	—
151	D₂₈	—	4	2	no	—
152	C₄×D₇	—	2	2	no	—
153	C₄×D₇	—	2	4	no	—
154	C₄×D₇	—	4	2	no	—
155	C₄×D₇	C₃×D₄	1	4	yes	complemented
156	Dic₁₄	—	2	2	no	—
157	C₃×#41	—	14	4	no	—
158	C₃×#41	—	14	4	no	—
159	C₂×C₃×Q₈	—	7	1	no	—
160	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic
161	C₂×C₃×D₄	—	7	1	no	—
162	C₂×C₃×D₄	—	7	1	no	—
163	C₂×C₃×D₄	—	7	2	no	—
164	C₂×C₃×D₄	—	7	1	no	—
165	C₂×C₃×D₄	—	7	2	no	—
166	C₂×C₃×D₄	—	7	1	no	—
167	C₂×C₃×D₄	—	7	2	no	—
168	C₂²×C₃×C₄	—	7	1	no	—
169	C₂²×C₃×C₄	—	7	2	no	—
170	C₂²×C₃×C₄	—	7	1	no	—
171	C₂²×C₃×C₄	—	7	2	no	—
172	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
173	C₃×C₄⋊C₄	—	7	2	no	—
174	C₃×C₄⋊C₄	—	7	2	no	—
175	C₃×C₄⋊C₄	—	7	1	no	—
176	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
177	C₃×C₄⋊C₄	C₂×D₇	1	2	yes	—
178	C₃×C₂²⋊C₄	—	7	2	no	—
179	C₃×C₂²⋊C₄	—	7	2	no	—
180	C₃×C₂²⋊C₄	—	7	2	no	—
181	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	—
182	C₂×C₃×C₇	—	4	1	no	—
183	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₃×C₇	2₋¹⁺⁴	1	1	yes	characteristic
186	C₃×D₇	—	2	2	no	—
187	C₃×D₇	—	4	2	no	—
188	C₃×D₇	—	4	1	no	—
189	C₂×#41	—	7	1	no	—
190	C₂×#41	—	7	1	no	—
191	C₂²⋊Q₈	—	7	1	no	—
192	C₂²⋊Q₈	—	7	2	no	—
193	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, complemented
194	#121	—	7	1	no	—
195	#121	—	7	1	no	—
196	#121	—	7	2	no	—
197	#121	—	7	2	no	—
198	#121	—	7	2	no	—
199	C₂×C₄⋊C₄	—	7	1	no	—
200	C₂²×C₇	—	2	1	no	—
201	C₂²×C₇	—	2	1	no	—
202	C₂²×C₇	—	2	1	no	—
203	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
204	C₂×D₇	—	2	1	no	—
205	C₂×D₇	—	2	1	no	—
206	C₂×D₇	—	2	2	no	—
207	C₂×D₇	—	2	1	no	—
208	C₂×D₇	—	2	1	no	—
209	C₂×D₇	—	2	2	no	—
210	C₂×D₇	—	2	2	no	—
211	C₂×D₇	—	2	1	no	—
212	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
213	C₄×C₇	—	2	1	no	—
214	C₄×C₇	—	2	2	no	—
215	C₄×C₇	—	2	2	no	—
216	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
217	Dic₇	—	2	1	no	—
218	Dic₇	—	2	2	no	—
219	Dic₇	C₂×C₃×D₄	1	2	yes	—
220	C₂³×C₃	—	7	1	no	—
221	C₂³×C₃	—	7	1	no	—
222	C₂³×C₃	—	7	2	no	—
223	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
224	C₃×Q₈	—	2	2	no	—
225	C₃×Q₈	—	14	2	no	—
226	C₃×D₄	—	14	2	no	—
227	C₃×D₄	—	14	4	no	—
228	C₃×D₄	—	14	2	no	—
229	C₃×D₄	—	14	2	no	—
230	C₃×D₄	—	14	2	no	—
231	C₃×D₄	—	28	2	no	—
232	C₃×D₄	—	28	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	7	1	no	—
235	C₂×C₃×C₄	—	7	4	no	—
236	C₂×C₃×C₄	—	7	2	no	—
237	C₂×C₃×C₄	—	7	1	no	—
238	C₂×C₃×C₄	—	14	4	no	—
239	C₂×C₃×C₄	—	14	2	no	—
240	C₂×C₃×C₄	—	28	2	no	—
241	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
243	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
244	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
245	C₃×C₇	#537	1	1	yes	characteristic, complemented, Hall
246	#41	—	14	4	no	—
247	#41	—	14	4	no	—
248	C₂×Q₈	—	7	1	no	—
249	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic
250	C₂×D₄	—	7	1	no	—
251	C₂×D₄	—	7	1	no	—
252	C₂×D₄	—	7	2	no	—
253	C₂×D₄	—	7	1	no	—
254	C₂×D₄	—	7	2	no	—
255	C₂×D₄	—	7	1	no	—
256	C₂×D₄	—	7	2	no	—
257	C₂²×C₄	—	7	1	no	—
258	C₂²×C₄	—	7	2	no	—
259	C₂²×C₄	—	7	1	no	—
260	C₂²×C₄	—	7	2	no	—
261	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
262	C₄⋊C₄	—	7	2	no	—
263	C₄⋊C₄	—	7	2	no	—
264	C₄⋊C₄	—	7	1	no	—
265	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic
266	C₄⋊C₄	C₂×C₃×D₇	1	2	yes	—
267	C₂²⋊C₄	—	7	2	no	—
268	C₂²⋊C₄	—	7	2	no	—
269	C₂²⋊C₄	—	7	2	no	—
270	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	—
271	C₂×C₇	—	4	1	no	—
272	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
273	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₇	C₃×2₋¹⁺⁴	1	1	yes	characteristic
275	D₇	—	2	2	no	—
276	D₇	—	4	2	no	—
277	D₇	—	4	1	no	—
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	7	2	no	—
282	C₂²×C₃	—	14	1	no	—
283	C₂²×C₃	—	14	1	no	—
284	C₂²×C₃	—	14	2	no	—
285	C₂²×C₃	—	14	1	no	—
286	C₂²×C₃	—	14	1	no	—
287	C₂²×C₃	—	14	2	no	—
288	C₂²×C₃	—	14	1	no	—
289	C₂²×C₃	—	14	2	no	—
290	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	7	2	no	—
295	C₃×C₄	—	14	1	no	—
296	C₃×C₄	—	14	2	no	—
297	C₃×C₄	D₄×D₇	1	2	yes	—
298	C₂³	—	7	1	no	—
299	C₂³	—	7	1	no	—
300	C₂³	—	7	2	no	—
301	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
302	Q₈	—	2	2	no	—
303	Q₈	—	14	2	no	—
304	D₄	—	14	2	no	—
305	D₄	—	14	4	no	—
306	D₄	—	14	2	no	—
307	D₄	—	14	2	no	—
308	D₄	—	14	2	no	—
309	D₄	—	28	2	no	—
310	D₄	—	28	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	7	1	no	—
313	C₂×C₄	—	7	4	no	—
314	C₂×C₄	—	7	2	no	—
315	C₂×C₄	—	7	1	no	—
316	C₂×C₄	—	14	4	no	—
317	C₂×C₄	—	14	2	no	—
318	C₂×C₄	—	28	2	no	—
319	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
320	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
321	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
322	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
323	C₇	C₃×#537	1	1	yes	characteristic, complemented, Sylow
324	C₂×C₃	—	4	1	no	—
325	C₂×C₃	—	14	2	no	—
326	C₂×C₃	—	28	2	no	—
327	C₂×C₃	—	28	1	no	—
328	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
329	C₂×C₃	#6551	1	1	yes	characteristic
330	C₂×C₃	#6553	1	1	yes	characteristic
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	7	2	no	—
335	C₂²	—	14	1	no	—
336	C₂²	—	14	1	no	—
337	C₂²	—	14	2	no	—
338	C₂²	—	14	1	no	—
339	C₂²	—	14	1	no	—
340	C₂²	—	14	2	no	—
341	C₂²	—	14	1	no	—
342	C₂²	—	14	2	no	—
343	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	7	2	no	—
348	C₄	—	14	1	no	—
349	C₄	—	14	2	no	—
350	C₄	C₃×D₄×D₇	1	2	yes	—
351	C₃	#90320	1	1	yes	characteristic, direct product factor, Sylow
352	C₂	—	4	1	no	—
353	C₂	—	14	2	no	—
354	C₂	—	28	2	no	—
355	C₂	—	28	1	no	—
356	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
357	C₂	C₃×#6551	1	1	yes	characteristic
358	C₂	C₃×#6553	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₃×#537
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1161	C₂	semidirect
2. C₂×C₃×#1157	C₂	semidirect
3. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
4. C₃×#6509	C₂	semidirect
5. C₃×#6493	C₂	semidirect
6. C₃×#6459	C₂	semidirect
7. C₃×#6458	C₂	semidirect
8. C₃×#6458	C₂	semidirect
9. C₃×D₇×C₄⋊C₄	C₂	semidirect
10. C₃×#6447	C₂	semidirect
11. C₃×#6447	C₂	semidirect
12. #90320	C₃	direct (N × H)
38. C₂×#1161	C₂×C₃	semidirect
39. C₂×#1157	C₂×C₃	semidirect
40. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
41. #6509	C₂×C₃	semidirect
42. #6493	C₂×C₃	semidirect
43. #6459	C₂×C₃	semidirect
44. #6458	C₂×C₃	semidirect
45. #6458	C₂×C₃	semidirect
46. D₇×C₄⋊C₄	C₂×C₃	semidirect
47. #6447	C₂×C₃	semidirect
48. #6447	C₂×C₃	semidirect
73. C₃×C₄×D₇	D₄	semidirect
104. C₃×C₂²⋊Q₈	D₇	semidirect
155. C₄×D₇	C₃×D₄	semidirect
193. C₂²⋊Q₈	C₃×D₇	semidirect
245. C₃×C₇	#537	semidirect
323. C₇	C₃×#537	semidirect
351. C₃	#90320	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#1161	2
C₂×C₃×#1157	2
C₃×C₇×C₂²⋊Q₈	2
C₃×#6509	2
C₃×#6493	2
C₃×#6459	2
C₃×#6458	2
C₃×D₇×C₄⋊C₄	2
C₃×#6447	2
#90320	3
C₃×#537	7

Subgroups — C3×#90320 #13060975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90320 #13060975