Subgroups — C₃×#3484 #87368

Order 384.

1900 conjugacy classes of subgroups.

The subgroup lattice has 290 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	C₂³×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#546	C₂	1	8	yes	maximal, complemented
4	C₃×D₄²	C₂	1	8	yes	maximal, complemented
5	C₃×#535	C₂	1	2	yes	maximal, complemented
6	C₃×#534	C₂	1	4	yes	maximal, complemented
7	C₃×#525	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#120	C₂	1	4	yes	maximal, complemented
9	C₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
10	#3484	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂⁵×C₃	C₂²	1	2	yes	complemented
12	C₃×H(5,𝔽₂)	—	2	8	no	—
13	C₂×C₃×#41	C₂²	1	2	yes	complemented
14	C₂×C₃×#41	C₂²	1	4	yes	complemented
15	C₂²×C₃×D₄	—	2	8	no	—
16	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×D₄	C₂²	1	8	yes	complemented
20	C₂²×C₃×D₄	C₂²	1	4	yes	complemented
21	C₂²×C₃×D₄	C₂²	1	4	yes	complemented
22	C₂²×C₃×D₄	C₂²	1	8	yes	complemented
23	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃×#127	C₂²	1	4	yes	complemented
25	C₃×#124	C₂²	1	4	yes	complemented
26	C₃×#123	C₂²	1	4	yes	complemented
27	C₃×#123	C₂²	1	8	yes	complemented
28	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
29	C₃×#121	C₂²	1	4	yes	complemented
30	C₃×#121	C₂²	1	16	yes	complemented
31	C₃×#121	C₂²	1	8	yes	complemented
32	C₃×#120	C₂²	1	4	yes	complemented
33	C₃×#120	C₂²	1	8	yes	complemented
34	C₃×#120	C₂²	1	16	yes	complemented
35	C₃×#120	C₂²	1	8	yes	complemented
36	C₃×C₄×D₄	C₂²	1	8	yes	complemented
37	C₃×C₄×D₄	C₂²	1	8	yes	complemented
38	C₃×#117	C₂²	1	2	yes	complemented
39	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
40	C₂×C₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₂×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂³×D₄	C₂×C₃	1	1	yes	characteristic, complemented
43	#546	C₂×C₃	1	8	yes	complemented
44	D₄²	C₂×C₃	1	8	yes	complemented
45	#535	C₂×C₃	1	2	yes	complemented
46	#534	C₂×C₃	1	4	yes	complemented
47	#525	C₂×C₃	1	2	yes	complemented
48	C₂×#120	C₂×C₃	1	4	yes	complemented
49	#518	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂⁴×C₃	—	2	8	no	—
51	C₂⁴×C₃	—	4	8	no	—
52	C₂⁴×C₃	C₂³	1	1	yes	characteristic
53	C₂⁴×C₃	C₂³	1	8	yes	—
54	C₂⁴×C₃	C₂³	1	2	yes	—
55	C₂⁴×C₃	C₂³	1	2	yes	—
56	C₂⁴×C₃	C₂³	1	4	yes	complemented
57	C₃×#41	—	2	16	no	—
58	C₃×#41	—	2	8	no	—
59	C₂×C₃×Q₈	C₂³	1	2	yes	complemented
60	C₂×C₃×D₄	—	2	8	no	—
61	C₂×C₃×D₄	—	2	16	no	—
62	C₂×C₃×D₄	—	2	32	no	—
63	C₂×C₃×D₄	—	2	16	no	—
64	C₂×C₃×D₄	—	2	4	no	—
65	C₂×C₃×D₄	—	4	16	no	—
66	C₂×C₃×D₄	D₄	1	8	yes	complemented
67	C₂×C₃×D₄	C₂³	1	8	yes	—
68	C₂×C₃×D₄	C₂³	1	4	yes	—
69	C₂×C₃×D₄	C₂³	1	8	yes	—
70	C₂×C₃×D₄	C₂³	1	4	yes	—
71	C₂×C₃×D₄	C₂³	1	4	yes	—
72	C₂×C₃×D₄	C₂³	1	8	yes	complemented
73	C₂×C₃×D₄	C₂³	1	2	yes	complemented
74	C₂×C₃×D₄	C₂³	1	16	yes	complemented
75	C₂²×C₃×C₄	—	2	4	no	—
76	C₂²×C₃×C₄	C₂³	1	4	yes	—
77	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₂³	1	4	yes	complemented
80	C₂²×C₃×C₄	C₂³	1	4	yes	complemented
81	C₂²×C₃×C₄	C₂³	1	8	yes	complemented
82	C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
83	C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
84	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
87	C₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
88	C₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
89	C₃×C₄²	C₂³	1	4	yes	complemented
90	C₂⁵	C₂²×C₃	1	2	yes	complemented
91	H(5,𝔽₂)	—	2	8	no	—
92	C₂×#41	C₂²×C₃	1	2	yes	complemented
93	C₂×#41	C₂²×C₃	1	4	yes	complemented
94	C₂²×D₄	—	2	8	no	—
95	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂²×D₄	C₂²×C₃	1	2	yes	complemented
97	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₂²×D₄	C₂²×C₃	1	8	yes	complemented
99	C₂²×D₄	C₂²×C₃	1	4	yes	complemented
100	C₂²×D₄	C₂²×C₃	1	4	yes	complemented
101	C₂²×D₄	C₂²×C₃	1	8	yes	complemented
102	C₂³×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
103	#127	C₂²×C₃	1	4	yes	complemented
104	#124	C₂²×C₃	1	4	yes	complemented
105	#123	C₂²×C₃	1	4	yes	complemented
106	#123	C₂²×C₃	1	8	yes	complemented
107	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
108	#121	C₂²×C₃	1	4	yes	complemented
109	#121	C₂²×C₃	1	16	yes	complemented
110	#121	C₂²×C₃	1	8	yes	complemented
111	#120	C₂²×C₃	1	4	yes	complemented
112	#120	C₂²×C₃	1	8	yes	complemented
113	#120	C₂²×C₃	1	16	yes	complemented
114	#120	C₂²×C₃	1	8	yes	complemented
115	C₄×D₄	C₂²×C₃	1	8	yes	complemented
116	C₄×D₄	C₂²×C₃	1	8	yes	complemented
117	#117	C₂²×C₃	1	2	yes	complemented
118	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
119	C₂×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
120	C₂³×C₃	—	2	2	no	—
121	C₂³×C₃	—	2	4	no	—
122	C₂³×C₃	—	2	16	no	—
123	C₂³×C₃	—	2	4	no	—
124	C₂³×C₃	—	2	16	no	—
125	C₂³×C₃	—	2	8	no	—
126	C₂³×C₃	—	4	4	no	—
127	C₂³×C₃	—	4	8	no	—
128	C₂³×C₃	—	4	4	no	—
129	C₂³×C₃	—	4	8	no	—
130	C₂³×C₃	—	4	32	no	—
131	C₂³×C₃	C₂×D₄	1	8	yes	complemented
132	C₂³×C₃	C₂⁴	1	4	yes	—
133	C₂³×C₃	C₂⁴	1	4	yes	—
134	C₂³×C₃	C₂⁴	1	1	yes	characteristic
135	C₂³×C₃	C₂⁴	1	4	yes	—
136	C₂³×C₃	C₂⁴	1	2	yes	—
137	C₃×Q₈	—	2	4	no	—
138	C₃×D₄	—	2	16	no	—
139	C₃×D₄	—	2	8	no	—
140	C₃×D₄	—	2	16	no	—
141	C₃×D₄	—	2	16	no	—
142	C₃×D₄	—	2	8	no	—
143	C₃×D₄	—	2	4	no	—
144	C₃×D₄	—	4	16	no	—
145	C₃×D₄	C₂×D₄	1	16	yes	complemented
146	C₂×C₃×C₄	—	2	2	no	—
147	C₂×C₃×C₄	—	2	8	no	—
148	C₂×C₃×C₄	—	2	8	no	—
149	C₂×C₃×C₄	—	2	8	no	—
150	C₂×C₃×C₄	—	4	8	no	—
151	C₂×C₃×C₄	C₂×D₄	1	4	yes	complemented
152	C₂×C₃×C₄	C₂⁴	1	8	yes	—
153	C₂×C₃×C₄	C₂⁴	1	4	yes	—
154	C₂×C₃×C₄	C₂⁴	1	2	yes	—
155	C₂×C₃×C₄	C₂⁴	1	2	yes	—
156	C₂⁴	—	2	8	no	—
157	C₂⁴	—	4	8	no	—
158	C₂⁴	C₂³×C₃	1	1	yes	characteristic
159	C₂⁴	C₂³×C₃	1	8	yes	—
160	C₂⁴	C₂³×C₃	1	2	yes	—
161	C₂⁴	C₂³×C₃	1	2	yes	—
162	C₂⁴	C₂³×C₃	1	4	yes	complemented
163	#41	—	2	16	no	—
164	#41	—	2	8	no	—
165	C₂×Q₈	C₂³×C₃	1	2	yes	complemented
166	C₂×D₄	—	2	8	no	—
167	C₂×D₄	—	2	16	no	—
168	C₂×D₄	—	2	32	no	—
169	C₂×D₄	—	2	16	no	—
170	C₂×D₄	—	2	4	no	—
171	C₂×D₄	—	4	16	no	—
172	C₂×D₄	C₃×D₄	1	8	yes	complemented
173	C₂×D₄	C₂³×C₃	1	8	yes	—
174	C₂×D₄	C₂³×C₃	1	4	yes	—
175	C₂×D₄	C₂³×C₃	1	8	yes	—
176	C₂×D₄	C₂³×C₃	1	4	yes	—
177	C₂×D₄	C₂³×C₃	1	4	yes	—
178	C₂×D₄	C₂³×C₃	1	8	yes	complemented
179	C₂×D₄	C₂³×C₃	1	2	yes	complemented
180	C₂×D₄	C₂³×C₃	1	16	yes	complemented
181	C₂²×C₄	—	2	4	no	—
182	C₂²×C₄	C₂³×C₃	1	4	yes	—
183	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄	C₂³×C₃	1	4	yes	complemented
186	C₂²×C₄	C₂³×C₃	1	4	yes	complemented
187	C₂²×C₄	C₂³×C₃	1	8	yes	complemented
188	C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
189	C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
190	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
191	C₂²⋊C₄	C₂³×C₃	1	8	yes	—
192	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
193	C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
194	C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
195	C₄²	C₂³×C₃	1	4	yes	complemented
196	C₂²×C₃	—	2	8	no	—
197	C₂²×C₃	—	2	2	no	—
198	C₂²×C₃	—	2	8	no	—
199	C₂²×C₃	—	2	2	no	—
200	C₂²×C₃	—	2	2	no	—
201	C₂²×C₃	—	2	4	no	—
202	C₂²×C₃	—	2	4	no	—
203	C₂²×C₃	—	2	8	no	—
204	C₂²×C₃	—	2	8	no	—
205	C₂²×C₃	—	4	8	no	—
206	C₂²×C₃	—	4	32	no	—
207	C₂²×C₃	—	4	8	no	—
208	C₂²×C₃	—	8	8	no	—
209	C₂²×C₃	C₂²×D₄	1	2	yes	—
210	C₂²×C₃	C₂²×D₄	1	8	yes	—
211	C₂²×C₃	H(5,𝔽₂)	1	4	yes	complemented
212	C₂²×C₃	C₂⁵	1	1	yes	characteristic
213	C₃×C₄	—	2	2	no	—
214	C₃×C₄	—	2	4	no	—
215	C₃×C₄	—	2	8	no	—
216	C₃×C₄	C₂²×D₄	1	4	yes	—
217	C₂³	—	2	2	no	—
218	C₂³	—	2	4	no	—
219	C₂³	—	2	16	no	—
220	C₂³	—	2	4	no	—
221	C₂³	—	2	16	no	—
222	C₂³	—	2	8	no	—
223	C₂³	—	4	4	no	—
224	C₂³	—	4	8	no	—
225	C₂³	—	4	4	no	—
226	C₂³	—	4	8	no	—
227	C₂³	—	4	32	no	—
228	C₂³	C₂×C₃×D₄	1	8	yes	complemented
229	C₂³	C₂⁴×C₃	1	4	yes	—
230	C₂³	C₂⁴×C₃	1	4	yes	—
231	C₂³	C₂⁴×C₃	1	1	yes	characteristic
232	C₂³	C₂⁴×C₃	1	4	yes	—
233	C₂³	C₂⁴×C₃	1	2	yes	—
234	Q₈	—	2	4	no	—
235	D₄	—	2	16	no	—
236	D₄	—	2	8	no	—
237	D₄	—	2	16	no	—
238	D₄	—	2	16	no	—
239	D₄	—	2	8	no	—
240	D₄	—	2	4	no	—
241	D₄	—	4	16	no	—
242	D₄	C₂×C₃×D₄	1	16	yes	complemented
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	8	no	—
245	C₂×C₄	—	2	8	no	—
246	C₂×C₄	—	2	8	no	—
247	C₂×C₄	—	4	8	no	—
248	C₂×C₄	C₂×C₃×D₄	1	4	yes	complemented
249	C₂×C₄	C₂⁴×C₃	1	8	yes	—
250	C₂×C₄	C₂⁴×C₃	1	4	yes	—
251	C₂×C₄	C₂⁴×C₃	1	2	yes	—
252	C₂×C₄	C₂⁴×C₃	1	2	yes	—
253	C₂×C₃	—	2	2	no	—
254	C₂×C₃	—	2	4	no	—
255	C₂×C₃	—	2	8	no	—
256	C₂×C₃	—	4	4	no	—
257	C₂×C₃	—	4	4	no	—
258	C₂×C₃	C₂³×D₄	1	1	yes	characteristic
259	C₂×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
260	C₂²	—	2	8	no	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	8	no	—
263	C₂²	—	2	2	no	—
264	C₂²	—	2	2	no	—
265	C₂²	—	2	4	no	—
266	C₂²	—	2	4	no	—
267	C₂²	—	2	8	no	—
268	C₂²	—	2	8	no	—
269	C₂²	—	4	8	no	—
270	C₂²	—	4	32	no	—
271	C₂²	—	4	8	no	—
272	C₂²	—	8	8	no	—
273	C₂²	C₂²×C₃×D₄	1	2	yes	—
274	C₂²	C₂²×C₃×D₄	1	8	yes	—
275	C₂²	C₃×H(5,𝔽₂)	1	4	yes	complemented
276	C₂²	C₂⁵×C₃	1	1	yes	characteristic
277	C₄	—	2	2	no	—
278	C₄	—	2	4	no	—
279	C₄	—	2	8	no	—
280	C₄	C₂²×C₃×D₄	1	4	yes	—
281	C₃	#3484	1	1	yes	characteristic, direct product factor, Sylow
282	C₂	—	2	2	no	—
283	C₂	—	2	4	no	—
284	C₂	—	2	8	no	—
285	C₂	—	4	4	no	—
286	C₂	—	4	4	no	—
287	C₂	C₂³×C₃×D₄	1	1	yes	characteristic
288	C₂	C₂×C₃×H(5,𝔽₂)	1	2	yes	—

	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. C₂³×C₃×D₄	C₂	semidirect
3. C₃×#546	C₂	semidirect
4. C₃×D₄²	C₂	semidirect
5. C₃×#535	C₂	semidirect
6. C₃×#534	C₂	semidirect
7. C₃×#525	C₂	semidirect
8. C₂×C₃×#120	C₂	semidirect
9. C₃×#518	C₂	semidirect
10. #3484	C₃	direct (N × H)
11. C₂⁵×C₃	C₂²	semidirect
13. C₂×C₃×#41	C₂²	semidirect
14. C₂×C₃×#41	C₂²	semidirect
17. C₂²×C₃×D₄	C₂²	semidirect
18. C₂²×C₃×D₄	C₂²	semidirect
19. C₂²×C₃×D₄	C₂²	semidirect
20. C₂²×C₃×D₄	C₂²	semidirect
21. C₂²×C₃×D₄	C₂²	semidirect
22. C₂²×C₃×D₄	C₂²	semidirect
23. C₂³×C₃×C₄	C₂²	semidirect
24. C₃×#127	C₂²	semidirect
25. C₃×#124	C₂²	semidirect
26. C₃×#123	C₂²	semidirect
27. C₃×#123	C₂²	semidirect
28. C₃×C₂²⋊Q₈	C₂²	semidirect
29. C₃×#121	C₂²	semidirect
30. C₃×#121	C₂²	semidirect
31. C₃×#121	C₂²	semidirect
32. C₃×#120	C₂²	semidirect
33. C₃×#120	C₂²	semidirect
34. C₃×#120	C₂²	semidirect
35. C₃×#120	C₂²	semidirect
36. C₃×C₄×D₄	C₂²	semidirect
37. C₃×C₄×D₄	C₂²	semidirect
38. C₃×#117	C₂²	semidirect
39. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
41. C₂×H(5,𝔽₂)	C₂×C₃	semidirect
42. C₂³×D₄	C₂×C₃	semidirect
43. #546	C₂×C₃	semidirect
44. D₄²	C₂×C₃	semidirect
45. #535	C₂×C₃	semidirect
46. #534	C₂×C₃	semidirect
47. #525	C₂×C₃	semidirect
48. C₂×#120	C₂×C₃	semidirect
49. #518	C₂×C₃	semidirect
56. C₂⁴×C₃	C₂³	semidirect
59. C₂×C₃×Q₈	C₂³	semidirect
66. C₂×C₃×D₄	D₄	semidirect
72. C₂×C₃×D₄	C₂³	semidirect
73. C₂×C₃×D₄	C₂³	semidirect
74. C₂×C₃×D₄	C₂³	semidirect
79. C₂²×C₃×C₄	C₂³	semidirect
80. C₂²×C₃×C₄	C₂³	semidirect
81. C₂²×C₃×C₄	C₂³	semidirect
82. C₃×C₄⋊C₄	C₂³	semidirect
83. C₃×C₄⋊C₄	C₂³	semidirect
86. C₃×C₂²⋊C₄	C₂³	semidirect
87. C₃×C₂²⋊C₄	C₂³	semidirect
88. C₃×C₂²⋊C₄	C₂³	semidirect
89. C₃×C₄²	C₂³	semidirect
90. C₂⁵	C₂²×C₃	semidirect
92. C₂×#41	C₂²×C₃	semidirect
93. C₂×#41	C₂²×C₃	semidirect
96. C₂²×D₄	C₂²×C₃	semidirect
97. C₂²×D₄	C₂²×C₃	semidirect
98. C₂²×D₄	C₂²×C₃	semidirect
99. C₂²×D₄	C₂²×C₃	semidirect
100. C₂²×D₄	C₂²×C₃	semidirect
101. C₂²×D₄	C₂²×C₃	semidirect
102. C₂³×C₄	C₂²×C₃	semidirect
103. #127	C₂²×C₃	semidirect
104. #124	C₂²×C₃	semidirect
105. #123	C₂²×C₃	semidirect
106. #123	C₂²×C₃	semidirect
107. C₂²⋊Q₈	C₂²×C₃	semidirect
108. #121	C₂²×C₃	semidirect
109. #121	C₂²×C₃	semidirect
110. #121	C₂²×C₃	semidirect
111. #120	C₂²×C₃	semidirect
112. #120	C₂²×C₃	semidirect
113. #120	C₂²×C₃	semidirect
114. #120	C₂²×C₃	semidirect
115. C₄×D₄	C₂²×C₃	semidirect
116. C₄×D₄	C₂²×C₃	semidirect
117. #117	C₂²×C₃	semidirect
118. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
119. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
131. C₂³×C₃	C₂×D₄	semidirect
145. C₃×D₄	C₂×D₄	semidirect
151. C₂×C₃×C₄	C₂×D₄	semidirect
162. C₂⁴	C₂³×C₃	semidirect
165. C₂×Q₈	C₂³×C₃	semidirect
172. C₂×D₄	C₃×D₄	semidirect
178. C₂×D₄	C₂³×C₃	semidirect
179. C₂×D₄	C₂³×C₃	semidirect
180. C₂×D₄	C₂³×C₃	semidirect
185. C₂²×C₄	C₂³×C₃	semidirect
186. C₂²×C₄	C₂³×C₃	semidirect
187. C₂²×C₄	C₂³×C₃	semidirect
188. C₄⋊C₄	C₂³×C₃	semidirect
189. C₄⋊C₄	C₂³×C₃	semidirect
192. C₂²⋊C₄	C₂³×C₃	semidirect
193. C₂²⋊C₄	C₂³×C₃	semidirect
194. C₂²⋊C₄	C₂³×C₃	semidirect
195. C₄²	C₂³×C₃	semidirect
211. C₂²×C₃	H(5,𝔽₂)	semidirect
228. C₂³	C₂×C₃×D₄	semidirect
242. D₄	C₂×C₃×D₄	semidirect
248. C₂×C₄	C₂×C₃×D₄	semidirect
275. C₂²	C₃×H(5,𝔽₂)	semidirect
281. C₃	#3484	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
C₂³×C₃×D₄	2
C₃×#546	2
C₃×D₄²	2
C₃×#535	2
C₃×#534	2
C₃×#525	2
C₂×C₃×#120	2
C₃×#518	2
#3484	3

Subgroups — C3×#3484 #87368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3484 #87368