Subgroups — C₃×#3488 #87372

Order 384.

1658 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#550	C₂	1	2	yes	maximal, complemented
4	C₃×#548	C₂	1	2	yes	maximal, complemented
5	C₃×#546	C₂	1	6	yes	maximal, complemented
6	C₃×D₄²	C₂	1	6	yes	maximal, complemented
7	C₃×#537	C₂	1	3	yes	maximal, complemented
8	C₃×#535	C₂	1	3	yes	maximal, complemented
9	C₃×#525	C₂	1	3	yes	maximal, complemented
10	C₂×C₃×#121	C₂	1	3	yes	maximal, complemented
11	C₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
12	#3488	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×H(5,𝔽₂)	—	2	8	no	—
14	C₂×C₃×#41	—	2	8	no	—
15	C₂×C₃×#41	C₂²	1	1	yes	characteristic
16	C₂×C₃×#41	C₂²	1	3	yes	complemented
17	C₂×C₃×#41	C₂²	1	3	yes	complemented
18	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#41	C₂²	1	3	yes	complemented
20	C₂×C₃×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×D₄	C₂²	1	3	yes	complemented
23	C₂²×C₃×D₄	C₂²	1	3	yes	complemented
24	C₂²×C₃×D₄	C₂²	1	6	yes	complemented
25	C₂²×C₃×D₄	C₂²	1	6	yes	complemented
26	C₂³×C₃×C₄	C₂²	1	3	yes	complemented
27	C₃×#127	C₂²	1	6	yes	complemented
28	C₃×#124	C₂²	1	6	yes	complemented
29	C₃×#123	C₂²	1	6	yes	complemented
30	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
32	C₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
33	C₃×#121	C₂²	1	3	yes	complemented
34	C₃×#121	C₂²	1	6	yes	complemented
35	C₃×#121	C₂²	1	6	yes	complemented
36	C₃×#121	C₂²	1	6	yes	complemented
37	C₃×#121	C₂²	1	3	yes	complemented
38	C₃×#121	C₂²	1	12	yes	complemented
39	C₃×#121	C₂²	1	6	yes	complemented
40	C₃×#120	C₂²	1	6	yes	complemented
41	C₃×#120	C₂²	1	12	yes	complemented
42	C₃×C₄×Q₈	C₂²	1	2	yes	complemented
43	C₃×C₄×D₄	C₂²	1	6	yes	complemented
44	C₃×C₄×D₄	C₂²	1	6	yes	complemented
45	C₃×C₄×D₄	C₂²	1	6	yes	complemented
46	C₃×#117	C₂²	1	3	yes	complemented
47	C₂×C₃×C₄⋊C₄	C₂²	1	3	yes	complemented
48	C₂×C₃×C₂²⋊C₄	C₂²	1	6	yes	complemented
49	C₂×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂²×#41	C₂×C₃	1	1	yes	characteristic, complemented
51	#550	C₂×C₃	1	2	yes	complemented
52	#548	C₂×C₃	1	2	yes	complemented
53	#546	C₂×C₃	1	6	yes	complemented
54	D₄²	C₂×C₃	1	6	yes	complemented
55	#537	C₂×C₃	1	3	yes	complemented
56	#535	C₂×C₃	1	3	yes	complemented
57	#525	C₂×C₃	1	3	yes	complemented
58	C₂×#121	C₂×C₃	1	3	yes	complemented
59	#520	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂⁴×C₃	C₂³	1	3	yes	—
61	C₂⁴×C₃	C₂³	1	6	yes	—
62	C₃×#41	—	2	4	no	—
63	C₃×#41	—	2	8	no	—
64	C₃×#41	—	2	12	no	—
65	C₃×#41	—	2	12	no	—
66	C₃×#41	—	2	12	no	—
67	C₃×#41	D₄	1	8	yes	complemented
68	C₂×C₃×Q₈	—	2	4	no	—
69	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×Q₈	C₂³	1	3	yes	—
71	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×D₄	—	2	12	no	—
73	C₂×C₃×D₄	—	2	24	no	—
74	C₂×C₃×D₄	—	2	12	no	—
75	C₂×C₃×D₄	—	4	12	no	—
76	C₂×C₃×D₄	C₂³	1	6	yes	—
77	C₂×C₃×D₄	C₂³	1	6	yes	—
78	C₂×C₃×D₄	C₂³	1	6	yes	—
79	C₂×C₃×D₄	C₂³	1	3	yes	—
80	C₂×C₃×D₄	C₂³	1	6	yes	—
81	C₂×C₃×D₄	C₂³	1	3	yes	—
82	C₂×C₃×D₄	C₂³	1	6	yes	—
83	C₂×C₃×D₄	C₂³	1	12	yes	—
84	C₂×C₃×D₄	C₂³	1	3	yes	—
85	C₂²×C₃×C₄	—	2	12	no	—
86	C₂²×C₃×C₄	C₂³	1	3	yes	—
87	C₂²×C₃×C₄	C₂³	1	3	yes	—
88	C₂²×C₃×C₄	C₂³	1	3	yes	—
89	C₂²×C₃×C₄	C₂³	1	6	yes	—
90	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄	C₂³	1	3	yes	—
92	C₂²×C₃×C₄	C₂³	1	6	yes	—
93	C₂²×C₃×C₄	C₂³	1	3	yes	—
94	C₃×C₄⋊C₄	C₂³	1	3	yes	—
95	C₃×C₄⋊C₄	C₂³	1	6	yes	—
96	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₃×C₄⋊C₄	C₂³	1	6	yes	—
99	C₃×C₂²⋊C₄	C₂³	1	6	yes	—
100	C₃×C₂²⋊C₄	C₂³	1	12	yes	—
101	C₃×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₃×C₂²⋊C₄	C₂³	1	6	yes	—
104	C₃×C₂²⋊C₄	C₂³	1	6	yes	—
105	C₃×C₄²	C₂³	1	6	yes	—
106	H(5,𝔽₂)	—	2	8	no	—
107	C₂×#41	—	2	8	no	—
108	C₂×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂×#41	C₂²×C₃	1	3	yes	complemented
110	C₂×#41	C₂²×C₃	1	3	yes	complemented
111	C₂×#41	C₂²×C₃	1	3	yes	complemented
112	C₂×#41	C₂²×C₃	1	2	yes	complemented
113	C₂×#41	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂²×D₄	C₂²×C₃	1	3	yes	complemented
116	C₂²×D₄	C₂²×C₃	1	3	yes	complemented
117	C₂²×D₄	C₂²×C₃	1	6	yes	complemented
118	C₂²×D₄	C₂²×C₃	1	6	yes	complemented
119	C₂³×C₄	C₂²×C₃	1	3	yes	complemented
120	#127	C₂²×C₃	1	6	yes	complemented
121	#124	C₂²×C₃	1	6	yes	complemented
122	#123	C₂²×C₃	1	6	yes	complemented
123	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂²⋊Q₈	C₂²×C₃	1	3	yes	complemented
125	C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
126	#121	C₂²×C₃	1	3	yes	complemented
127	#121	C₂²×C₃	1	6	yes	complemented
128	#121	C₂²×C₃	1	6	yes	complemented
129	#121	C₂²×C₃	1	6	yes	complemented
130	#121	C₂²×C₃	1	3	yes	complemented
131	#121	C₂²×C₃	1	12	yes	complemented
132	#121	C₂²×C₃	1	6	yes	complemented
133	#120	C₂²×C₃	1	6	yes	complemented
134	#120	C₂²×C₃	1	12	yes	complemented
135	C₄×Q₈	C₂²×C₃	1	2	yes	complemented
136	C₄×D₄	C₂²×C₃	1	6	yes	complemented
137	C₄×D₄	C₂²×C₃	1	6	yes	complemented
138	C₄×D₄	C₂²×C₃	1	6	yes	complemented
139	#117	C₂²×C₃	1	3	yes	complemented
140	C₂×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
141	C₂×C₂²⋊C₄	C₂²×C₃	1	6	yes	complemented
142	C₂³×C₃	—	2	6	no	—
143	C₂³×C₃	—	2	6	no	—
144	C₂³×C₃	—	2	12	no	—
145	C₂³×C₃	—	4	3	no	—
146	C₂³×C₃	—	4	6	no	—
147	C₂³×C₃	—	4	6	no	—
148	C₂³×C₃	C₂⁴	1	6	yes	—
149	C₂³×C₃	C₂⁴	1	3	yes	—
150	C₂³×C₃	C₂⁴	1	3	yes	—
151	C₂³×C₃	C₂⁴	1	1	yes	characteristic
152	C₃×Q₈	—	2	6	no	—
153	C₃×Q₈	—	2	2	no	—
154	C₃×Q₈	C₂×D₄	1	4	yes	complemented
155	C₃×D₄	—	2	12	no	—
156	C₃×D₄	—	2	12	no	—
157	C₃×D₄	—	2	12	no	—
158	C₃×D₄	—	2	6	no	—
159	C₃×D₄	—	2	12	no	—
160	C₃×D₄	—	2	6	no	—
161	C₃×D₄	—	4	12	no	—
162	C₃×D₄	—	4	6	no	—
163	C₃×D₄	C₂×D₄	1	12	yes	complemented
164	C₂×C₃×C₄	—	2	6	no	—
165	C₂×C₃×C₄	—	2	2	no	—
166	C₂×C₃×C₄	—	2	6	no	—
167	C₂×C₃×C₄	—	2	6	no	—
168	C₂×C₃×C₄	—	2	6	no	—
169	C₂×C₃×C₄	—	2	12	no	—
170	C₂×C₃×C₄	—	4	6	no	—
171	C₂×C₃×C₄	C₂×D₄	1	12	yes	complemented
172	C₂×C₃×C₄	C₂⁴	1	2	yes	—
173	C₂×C₃×C₄	C₂⁴	1	6	yes	—
174	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
175	C₂×C₃×C₄	C₂⁴	1	3	yes	—
176	C₂×C₃×C₄	C₂⁴	1	2	yes	—
177	C₂×C₃×C₄	C₂⁴	1	3	yes	—
178	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
179	C₂⁴	C₂³×C₃	1	3	yes	—
180	C₂⁴	C₂³×C₃	1	6	yes	—
181	#41	—	2	4	no	—
182	#41	—	2	8	no	—
183	#41	—	2	12	no	—
184	#41	—	2	12	no	—
185	#41	—	2	12	no	—
186	#41	C₃×D₄	1	8	yes	complemented
187	C₂×Q₈	—	2	4	no	—
188	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×Q₈	C₂³×C₃	1	3	yes	—
190	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×D₄	—	2	12	no	—
192	C₂×D₄	—	2	24	no	—
193	C₂×D₄	—	2	12	no	—
194	C₂×D₄	—	4	12	no	—
195	C₂×D₄	C₂³×C₃	1	6	yes	—
196	C₂×D₄	C₂³×C₃	1	6	yes	—
197	C₂×D₄	C₂³×C₃	1	6	yes	—
198	C₂×D₄	C₂³×C₃	1	3	yes	—
199	C₂×D₄	C₂³×C₃	1	6	yes	—
200	C₂×D₄	C₂³×C₃	1	3	yes	—
201	C₂×D₄	C₂³×C₃	1	6	yes	—
202	C₂×D₄	C₂³×C₃	1	12	yes	—
203	C₂×D₄	C₂³×C₃	1	3	yes	—
204	C₂²×C₄	—	2	12	no	—
205	C₂²×C₄	C₂³×C₃	1	3	yes	—
206	C₂²×C₄	C₂³×C₃	1	3	yes	—
207	C₂²×C₄	C₂³×C₃	1	3	yes	—
208	C₂²×C₄	C₂³×C₃	1	6	yes	—
209	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₄	C₂³×C₃	1	3	yes	—
211	C₂²×C₄	C₂³×C₃	1	6	yes	—
212	C₂²×C₄	C₂³×C₃	1	3	yes	—
213	C₄⋊C₄	C₂³×C₃	1	3	yes	—
214	C₄⋊C₄	C₂³×C₃	1	6	yes	—
215	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
216	C₄⋊C₄	C₂³×C₃	1	2	yes	—
217	C₄⋊C₄	C₂³×C₃	1	6	yes	—
218	C₂²⋊C₄	C₂³×C₃	1	6	yes	—
219	C₂²⋊C₄	C₂³×C₃	1	12	yes	—
220	C₂²⋊C₄	C₂³×C₃	1	6	yes	—
221	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
222	C₂²⋊C₄	C₂³×C₃	1	6	yes	—
223	C₂²⋊C₄	C₂³×C₃	1	6	yes	—
224	C₄²	C₂³×C₃	1	6	yes	—
225	C₂²×C₃	—	2	1	no	—
226	C₂²×C₃	—	2	3	no	—
227	C₂²×C₃	—	2	1	no	—
228	C₂²×C₃	—	2	3	no	—
229	C₂²×C₃	—	2	3	no	—
230	C₂²×C₃	—	2	6	no	—
231	C₂²×C₃	—	2	6	no	—
232	C₂²×C₃	—	2	3	no	—
233	C₂²×C₃	—	2	3	no	—
234	C₂²×C₃	—	2	6	no	—
235	C₂²×C₃	—	4	12	no	—
236	C₂²×C₃	—	8	12	no	—
237	C₂²×C₃	C₂²×D₄	1	6	yes	—
238	C₂²×C₃	H(5,𝔽₂)	1	2	yes	complemented
239	C₂²×C₃	C₂⁵	1	1	yes	characteristic
240	C₃×C₄	—	2	1	no	—
241	C₃×C₄	—	2	2	no	—
242	C₃×C₄	—	2	3	no	—
243	C₃×C₄	—	2	6	no	—
244	C₃×C₄	—	2	2	no	—
245	C₃×C₄	C₂²×D₄	1	2	yes	—
246	C₃×C₄	C₂²×D₄	1	6	yes	—
247	C₂³	—	2	6	no	—
248	C₂³	—	2	6	no	—
249	C₂³	—	2	12	no	—
250	C₂³	—	4	3	no	—
251	C₂³	—	4	6	no	—
252	C₂³	—	4	6	no	—
253	C₂³	C₂⁴×C₃	1	6	yes	—
254	C₂³	C₂⁴×C₃	1	3	yes	—
255	C₂³	C₂⁴×C₃	1	3	yes	—
256	C₂³	C₂⁴×C₃	1	1	yes	characteristic
257	Q₈	—	2	6	no	—
258	Q₈	—	2	2	no	—
259	Q₈	C₂×C₃×D₄	1	4	yes	complemented
260	D₄	—	2	12	no	—
261	D₄	—	2	12	no	—
262	D₄	—	2	12	no	—
263	D₄	—	2	6	no	—
264	D₄	—	2	12	no	—
265	D₄	—	2	6	no	—
266	D₄	—	4	12	no	—
267	D₄	—	4	6	no	—
268	D₄	C₂×C₃×D₄	1	12	yes	complemented
269	C₂×C₄	—	2	6	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	6	no	—
272	C₂×C₄	—	2	6	no	—
273	C₂×C₄	—	2	6	no	—
274	C₂×C₄	—	2	12	no	—
275	C₂×C₄	—	4	6	no	—
276	C₂×C₄	C₂×C₃×D₄	1	12	yes	complemented
277	C₂×C₄	C₂⁴×C₃	1	2	yes	—
278	C₂×C₄	C₂⁴×C₃	1	6	yes	—
279	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
280	C₂×C₄	C₂⁴×C₃	1	3	yes	—
281	C₂×C₄	C₂⁴×C₃	1	2	yes	—
282	C₂×C₄	C₂⁴×C₃	1	3	yes	—
283	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
284	C₂×C₃	—	2	2	no	—
285	C₂×C₃	—	2	6	no	—
286	C₂×C₃	—	4	3	no	—
287	C₂×C₃	—	4	6	no	—
288	C₂×C₃	C₂³×D₄	1	1	yes	characteristic
289	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₃	#585	1	1	yes	characteristic
291	C₂²	—	2	1	no	—
292	C₂²	—	2	3	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	3	no	—
295	C₂²	—	2	3	no	—
296	C₂²	—	2	6	no	—
297	C₂²	—	2	6	no	—
298	C₂²	—	2	3	no	—
299	C₂²	—	2	3	no	—
300	C₂²	—	2	6	no	—
301	C₂²	—	4	12	no	—
302	C₂²	—	8	12	no	—
303	C₂²	C₂²×C₃×D₄	1	6	yes	—
304	C₂²	C₃×H(5,𝔽₂)	1	2	yes	complemented
305	C₂²	C₂⁵×C₃	1	1	yes	characteristic
306	C₄	—	2	1	no	—
307	C₄	—	2	2	no	—
308	C₄	—	2	3	no	—
309	C₄	—	2	6	no	—
310	C₄	—	2	2	no	—
311	C₄	C₂²×C₃×D₄	1	2	yes	—
312	C₄	C₂²×C₃×D₄	1	6	yes	—
313	C₃	#3488	1	1	yes	characteristic, direct product factor, Sylow
314	C₂	—	2	2	no	—
315	C₂	—	2	6	no	—
316	C₂	—	4	3	no	—
317	C₂	—	4	6	no	—
318	C₂	C₂³×C₃×D₄	1	1	yes	characteristic
319	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
320	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×H(5,𝔽₂)	C₂	semidirect
2. C₂²×C₃×#41	C₂	semidirect
3. C₃×#550	C₂	semidirect
4. C₃×#548	C₂	semidirect
5. C₃×#546	C₂	semidirect
6. C₃×D₄²	C₂	semidirect
7. C₃×#537	C₂	semidirect
8. C₃×#535	C₂	semidirect
9. C₃×#525	C₂	semidirect
10. C₂×C₃×#121	C₂	semidirect
11. C₃×#520	C₂	semidirect
12. #3488	C₃	direct (N × H)
16. C₂×C₃×#41	C₂²	semidirect
17. C₂×C₃×#41	C₂²	semidirect
18. C₂×C₃×#41	C₂²	semidirect
19. C₂×C₃×#41	C₂²	semidirect
20. C₂×C₃×#41	C₂²	semidirect
21. C₂²×C₃×Q₈	C₂²	semidirect
22. C₂²×C₃×D₄	C₂²	semidirect
23. C₂²×C₃×D₄	C₂²	semidirect
24. C₂²×C₃×D₄	C₂²	semidirect
25. C₂²×C₃×D₄	C₂²	semidirect
26. C₂³×C₃×C₄	C₂²	semidirect
27. C₃×#127	C₂²	semidirect
28. C₃×#124	C₂²	semidirect
29. C₃×#123	C₂²	semidirect
30. C₃×C₂²⋊Q₈	C₂²	semidirect
31. C₃×C₂²⋊Q₈	C₂²	semidirect
32. C₃×C₂²⋊Q₈	C₂²	semidirect
33. C₃×#121	C₂²	semidirect
34. C₃×#121	C₂²	semidirect
35. C₃×#121	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
37. C₃×#121	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
39. C₃×#121	C₂²	semidirect
40. C₃×#120	C₂²	semidirect
41. C₃×#120	C₂²	semidirect
42. C₃×C₄×Q₈	C₂²	semidirect
43. C₃×C₄×D₄	C₂²	semidirect
44. C₃×C₄×D₄	C₂²	semidirect
45. C₃×C₄×D₄	C₂²	semidirect
46. C₃×#117	C₂²	semidirect
47. C₂×C₃×C₄⋊C₄	C₂²	semidirect
48. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
49. C₂×H(5,𝔽₂)	C₂×C₃	semidirect
50. C₂²×#41	C₂×C₃	semidirect
51. #550	C₂×C₃	semidirect
52. #548	C₂×C₃	semidirect
53. #546	C₂×C₃	semidirect
54. D₄²	C₂×C₃	semidirect
55. #537	C₂×C₃	semidirect
56. #535	C₂×C₃	semidirect
57. #525	C₂×C₃	semidirect
58. C₂×#121	C₂×C₃	semidirect
59. #520	C₂×C₃	semidirect
67. C₃×#41	D₄	semidirect
109. C₂×#41	C₂²×C₃	semidirect
110. C₂×#41	C₂²×C₃	semidirect
111. C₂×#41	C₂²×C₃	semidirect
112. C₂×#41	C₂²×C₃	semidirect
113. C₂×#41	C₂²×C₃	semidirect
114. C₂²×Q₈	C₂²×C₃	semidirect
115. C₂²×D₄	C₂²×C₃	semidirect
116. C₂²×D₄	C₂²×C₃	semidirect
117. C₂²×D₄	C₂²×C₃	semidirect
118. C₂²×D₄	C₂²×C₃	semidirect
119. C₂³×C₄	C₂²×C₃	semidirect
120. #127	C₂²×C₃	semidirect
121. #124	C₂²×C₃	semidirect
122. #123	C₂²×C₃	semidirect
123. C₂²⋊Q₈	C₂²×C₃	semidirect
124. C₂²⋊Q₈	C₂²×C₃	semidirect
125. C₂²⋊Q₈	C₂²×C₃	semidirect
126. #121	C₂²×C₃	semidirect
127. #121	C₂²×C₃	semidirect
128. #121	C₂²×C₃	semidirect
129. #121	C₂²×C₃	semidirect
130. #121	C₂²×C₃	semidirect
131. #121	C₂²×C₃	semidirect
132. #121	C₂²×C₃	semidirect
133. #120	C₂²×C₃	semidirect
134. #120	C₂²×C₃	semidirect
135. C₄×Q₈	C₂²×C₃	semidirect
136. C₄×D₄	C₂²×C₃	semidirect
137. C₄×D₄	C₂²×C₃	semidirect
138. C₄×D₄	C₂²×C₃	semidirect
139. #117	C₂²×C₃	semidirect
140. C₂×C₄⋊C₄	C₂²×C₃	semidirect
141. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
154. C₃×Q₈	C₂×D₄	semidirect
163. C₃×D₄	C₂×D₄	semidirect
171. C₂×C₃×C₄	C₂×D₄	semidirect
186. #41	C₃×D₄	semidirect
238. C₂²×C₃	H(5,𝔽₂)	semidirect
259. Q₈	C₂×C₃×D₄	semidirect
268. D₄	C₂×C₃×D₄	semidirect
276. C₂×C₄	C₂×C₃×D₄	semidirect
304. C₂²	C₃×H(5,𝔽₂)	semidirect
313. C₃	#3488	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×H(5,𝔽₂)	2
C₂²×C₃×#41	2
C₃×#550	2
C₃×#548	2
C₃×#546	2
C₃×D₄²	2
C₃×#537	2
C₃×#535	2
C₃×#525	2
C₂×C₃×#121	2
C₃×#520	2
#3488	3

Subgroups — C3×#3488 #87372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3488 #87372