Subgroups — C₃×#10596242 #13179522

Order 1728.

1736 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64367	C₂	1	2	yes	maximal, complemented
2	C₃³×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64160	C₂	1	2	yes	maximal, complemented
4	C₃×Q₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
5	C₃×#64124	C₂	1	4	yes	maximal, complemented
6	C₃×#64121	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#3746	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64110	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596242	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5771	—	3	4	no	maximal
11	C₃³×#41	C₂²	1	2	yes	—
12	C₃×Q₈×C₃⋊D₃	C₂²	1	4	yes	—
13	C₃×#3830	—	2	4	no	—
14	C₃×#3830	C₂²	1	4	yes	—
15	C₃×#3828	—	2	2	no	—
16	C₃×#3828	C₂²	1	1	yes	characteristic
17	C₂×C₃×#634	—	2	2	no	—
18	C₂×C₃×#634	C₂²	1	2	yes	—
19	C₃³×Q₁₆	C₂²	1	1	yes	characteristic
20	C₃³×SD₁₆	C₂²	1	2	yes	—
21	C₃³×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
23	C₃×#3756	C₂²	1	4	yes	—
24	C₃×#3754	C₂²	1	4	yes	—
25	C₃×#3748	C₂²	1	1	yes	characteristic
26	C₃×#3746	C₂²	1	2	yes	—
27	C₃×#3746	C₂²	1	2	yes	—
28	C₃×#3743	C₂²	1	2	yes	—
29	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	—
30	#64367	C₂×C₃	1	2	yes	complemented
31	C₃×#1010	—	3	8	no	—
32	C₃²×#135	—	2	4	no	—
33	C₃²×#135	D₃	1	4	yes	complemented
34	C₃²×#135	C₂×C₃	1	1	yes	characteristic, complemented
35	#64160	C₂×C₃	1	2	yes	complemented
36	Q₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
37	#64124	C₂×C₃	1	4	yes	complemented
38	#64121	C₂×C₃	1	2	yes	complemented
39	C₂×#3746	C₂×C₃	1	1	yes	characteristic, complemented
40	#64110	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#951	—	3	8	no	—
42	C₃×D₃×Q₁₆	—	3	8	no	—
43	C₃×#915	—	3	16	no	—
44	C₃×#912	—	3	8	no	—
45	C₂×C₃×Dic₁₂	—	3	4	no	—
46	C₃×#901	—	3	4	no	—
47	C₃³×Q₈	C₂³	1	2	yes	—
48	C₃³×D₄	—	2	2	no	—
49	C₃³×D₄	C₂³	1	2	yes	—
50	C₂×C₃³×C₄	—	2	2	no	—
51	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₃×#638	—	2	4	no	—
53	C₃×#638	D₄	1	2	yes	—
54	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
55	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
56	C₃×C₄⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
57	C₃×C₄×C₃⋊D₃	—	2	4	no	—
58	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
59	C₃×#634	—	2	2	no	—
60	C₃×#634	—	2	4	no	—
61	C₃×#634	D₄	1	1	yes	characteristic
62	C₃×#634	C₂³	1	4	yes	—
63	C₃³×C₈	C₂³	1	1	yes	characteristic
64	C₃³×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
66	C₃×#578	—	9	1	no	—
67	#5771	—	3	4	no	—
68	C₃²×#41	—	2	8	no	—
69	C₃²×#41	C₂×D₃	1	8	yes	—
70	C₃²×#41	C₂²×C₃	1	2	yes	—
71	Q₈×C₃⋊D₃	C₂²×C₃	1	4	yes	—
72	#3830	—	2	4	no	—
73	#3830	C₂²×C₃	1	4	yes	—
74	#3828	—	2	2	no	—
75	#3828	C₂²×C₃	1	1	yes	characteristic
76	C₂×#634	—	2	2	no	—
77	C₂×#634	C₂²×C₃	1	2	yes	—
78	C₃×D₃×Q₈	—	3	16	no	—
79	C₃×#237	—	3	16	no	—
80	C₃×#237	—	6	16	no	—
81	C₃×#235	—	3	4	no	—
82	C₃×#235	—	6	8	no	—
83	C₂×C₃×Dic₆	—	3	8	no	—
84	C₂×C₃×Dic₆	—	6	8	no	—
85	C₃²×Q₁₆	—	2	4	no	—
86	C₃²×Q₁₆	C₂×D₃	1	4	yes	—
87	C₃²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₃²×SD₁₆	—	2	8	no	—
89	C₃²×SD₁₆	C₂×D₃	1	8	yes	—
90	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
91	C₃²×D₈	—	2	4	no	—
92	C₃²×D₈	C₂×D₃	1	4	yes	—
93	C₃²×D₈	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃²×C₈	—	2	4	no	—
95	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
96	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
97	#3756	C₂²×C₃	1	4	yes	—
98	#3754	C₂²×C₃	1	4	yes	—
99	#3748	C₂²×C₃	1	1	yes	characteristic
100	#3746	C₂²×C₃	1	2	yes	—
101	#3746	C₂²×C₃	1	2	yes	—
102	#3743	C₂²×C₃	1	2	yes	—
103	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	—
104	C₃×#216	—	3	16	no	—
105	C₃×#214	—	3	16	no	—
106	C₃×#208	—	3	4	no	—
107	C₃×Dic₁₂	—	3	8	no	—
108	C₃×Dic₁₂	—	3	8	no	—
109	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
110	C₃×D₃×C₈	—	3	8	no	—
111	C₂²×C₃³	—	2	2	no	—
112	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
114	C₃³×C₄	—	2	2	no	—
115	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
116	C₃³×C₄	C₂⁴	1	1	yes	characteristic
117	C₃×C₃⋊Dic₃	—	2	4	no	—
118	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
119	C₃×2₋¹⁺⁴	—	9	2	no	—
120	#1010	—	3	8	no	—
121	C₃×#137	—	9	2	no	—
122	C₃×#137	—	9	4	no	—
123	C₃×#135	—	2	4	no	—
124	C₃×#135	—	9	2	no	—
125	C₃×#135	C₃×D₃	1	4	yes	complemented
126	C₃×#135	C₃⋊D₃	1	1	yes	characteristic, complemented
127	C₂×C₃×Q₁₆	—	9	2	no	—
128	C₂×C₃×Q₁₆	—	9	1	no	—
129	C₃×#131	—	9	1	no	—
130	#951	—	3	8	no	—
131	D₃×Q₁₆	—	3	8	no	—
132	#915	—	3	16	no	—
133	#912	—	3	8	no	—
134	C₂×Dic₁₂	—	3	4	no	—
135	#901	—	3	4	no	—
136	C₃²×Q₈	—	2	8	no	—
137	C₃²×Q₈	C₂²×D₃	1	8	yes	—
138	C₃²×Q₈	C₂³×C₃	1	2	yes	—
139	C₃²×D₄	—	2	2	no	—
140	C₃²×D₄	—	2	8	no	—
141	C₃²×D₄	—	2	8	no	—
142	C₃²×D₄	—	4	8	no	—
143	C₃²×D₄	C₂²×D₃	1	8	yes	—
144	C₃²×D₄	C₂³×C₃	1	2	yes	—
145	C₂×C₃²×C₄	—	2	2	no	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	8	no	—
148	C₂×C₃²×C₄	—	4	8	no	—
149	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
151	#638	—	2	4	no	—
152	#638	C₃×D₄	1	2	yes	—
153	C₂×C₃⋊Dic₃	—	2	2	no	—
154	C₂×C₃⋊Dic₃	—	2	4	no	—
155	C₄⋊(C₃⋊D₃)	C₃×D₄	1	1	yes	characteristic
156	C₄×C₃⋊D₃	—	2	4	no	—
157	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
158	#634	—	2	2	no	—
159	#634	—	2	4	no	—
160	#634	C₃×D₄	1	1	yes	characteristic
161	#634	C₂³×C₃	1	4	yes	—
162	C₃×#67	—	3	8	no	—
163	C₃×#67	—	6	16	no	—
164	C₂×C₃×Dic₃	—	6	16	no	—
165	C₂×C₃×Dic₃	—	6	8	no	—
166	C₃×D₁₂	—	3	4	no	—
167	C₃×C₄×D₃	—	3	8	no	—
168	C₃×C₄×D₃	—	6	16	no	—
169	C₃×Dic₆	—	3	4	no	—
170	C₃×Dic₆	—	3	16	no	—
171	C₃×Dic₆	—	6	16	no	—
172	C₃×Dic₆	—	6	8	no	—
173	C₃²×C₈	—	2	4	no	—
174	C₃²×C₈	—	2	4	no	—
175	C₃²×C₈	C₂²×D₃	1	4	yes	—
176	C₃²×C₈	C₂²×D₃	1	4	yes	—
177	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
178	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
179	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
180	C₃×C₃⋊C₈	—	3	8	no	—
181	#578	—	9	1	no	Sylow
182	C₂×C₃³	—	2	1	no	—
183	C₂×C₃³	—	4	2	no	—
184	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
185	C₃×C₃⋊D₃	—	2	2	no	—
186	C₃×#41	—	2	8	no	—
187	C₃×#41	—	9	1	no	—
188	C₃×#41	—	9	4	no	—
189	C₃×#41	—	18	2	no	—
190	C₃×#41	—	18	4	no	—
191	C₃×#41	C₂×C₃×D₃	1	8	yes	—
192	C₃×#41	C₂×C₃⋊D₃	1	2	yes	—
193	C₂×C₃×Q₈	—	9	4	no	—
194	C₂×C₃×Q₈	—	9	2	no	—
195	C₂×C₃×Q₈	—	18	2	no	—
196	D₃×Q₈	—	3	16	no	—
197	#237	—	3	16	no	—
198	#237	—	6	16	no	—
199	#235	—	3	4	no	—
200	#235	—	6	8	no	—
201	C₂×Dic₆	—	3	8	no	—
202	C₂×Dic₆	—	6	8	no	—
203	C₃×Q₁₆	—	2	4	no	—
204	C₃×Q₁₆	—	9	4	no	—
205	C₃×Q₁₆	—	9	2	no	—
206	C₃×Q₁₆	—	9	2	no	—
207	C₃×Q₁₆	C₂×C₃×D₃	1	4	yes	—
208	C₃×Q₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
209	C₃×SD₁₆	—	2	8	no	—
210	C₃×SD₁₆	—	9	4	no	—
211	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	—
212	C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	—
213	C₃×D₈	—	2	4	no	—
214	C₃×D₈	C₂×C₃×D₃	1	4	yes	—
215	C₃×D₈	C₂×C₃⋊D₃	1	1	yes	characteristic
216	C₃×M₁₆	—	9	1	no	—
217	C₃×M₁₆	—	9	2	no	—
218	C₂×C₃×C₈	—	2	4	no	—
219	C₂×C₃×C₈	—	9	2	no	—
220	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
221	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
222	#216	—	3	16	no	—
223	#214	—	3	16	no	—
224	#208	—	3	4	no	—
225	Dic₁₂	—	3	8	no	—
226	Dic₁₂	—	3	8	no	—
227	ΓL(1,𝔽₂₅)	—	3	8	no	—
228	D₃×C₈	—	3	8	no	—
229	C₂²×C₃²	—	2	2	no	—
230	C₂²×C₃²	—	2	4	no	—
231	C₂²×C₃²	—	2	8	no	—
232	C₂²×C₃²	—	4	8	no	—
233	C₂²×C₃²	D₃×D₄	1	4	yes	—
234	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
236	C₂×C₃×D₃	—	3	8	no	—
237	C₃²×C₄	—	2	2	no	—
238	C₃²×C₄	—	2	4	no	—
239	C₃²×C₄	—	2	4	no	—
240	C₃²×C₄	—	2	8	no	—
241	C₃²×C₄	—	4	8	no	—
242	C₃²×C₄	D₃×D₄	1	4	yes	—
243	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₃²×C₄	C₂³×D₃	1	4	yes	—
245	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
246	C₃⋊Dic₃	—	2	4	no	—
247	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
248	C₃×Dic₃	—	3	8	no	—
249	C₃×Dic₃	—	6	16	no	—
250	2₋¹⁺⁴	—	9	2	no	—
251	#137	—	9	2	no	—
252	#137	—	9	4	no	—
253	#135	—	9	2	no	—
254	#135	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
255	C₂×Q₁₆	—	9	2	no	—
256	C₂×Q₁₆	—	9	1	no	—
257	#131	—	9	1	no	—
258	C₃³	#578	1	1	yes	characteristic, complemented, Sylow
259	C₃×Q₈	—	2	8	no	—
260	C₃×Q₈	—	9	1	no	—
261	C₃×Q₈	—	9	4	no	—
262	C₃×Q₈	—	18	4	no	—
263	C₃×Q₈	—	18	2	no	—
264	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
265	C₃×Q₈	C₂²×C₃⋊D₃	1	2	yes	—
266	C₃×D₄	—	2	8	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	8	no	—
269	C₃×D₄	—	4	8	no	—
270	C₃×D₄	—	9	2	no	—
271	C₃×D₄	—	9	1	no	—
272	C₃×D₄	—	18	4	no	—
273	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
274	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	4	8	no	—
279	C₂×C₃×C₄	—	9	2	no	—
280	C₂×C₃×C₄	—	18	4	no	—
281	C₂×C₃×C₄	—	18	4	no	—
282	C₂×C₃×C₄	—	18	2	no	—
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
284	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
285	#67	—	3	8	no	—
286	#67	—	6	16	no	—
287	C₂×Dic₃	—	6	16	no	—
288	C₂×Dic₃	—	6	8	no	—
289	D₁₂	—	3	4	no	—
290	C₄×D₃	—	3	8	no	—
291	C₄×D₃	—	6	16	no	—
292	Dic₆	—	3	4	no	—
293	Dic₆	—	3	16	no	—
294	Dic₆	—	6	16	no	—
295	Dic₆	—	6	8	no	—
296	C₃×C₈	—	2	4	no	—
297	C₃×C₈	—	2	4	no	—
298	C₃×C₈	—	9	2	no	—
299	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
300	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
301	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
302	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
303	C₃⋊C₈	—	3	8	no	—
304	C₂×C₃²	—	2	1	no	—
305	C₂×C₃²	—	2	4	no	—
306	C₂×C₃²	—	2	4	no	—
307	C₂×C₃²	—	4	4	no	—
308	C₂×C₃²	—	4	2	no	—
309	C₂×C₃²	—	4	8	no	—
310	C₂×C₃²	—	8	8	no	—
311	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
312	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₃⋊D₃	—	2	2	no	—
314	C₃×D₃	—	6	8	no	—
315	#41	—	9	1	no	—
316	#41	—	9	4	no	—
317	#41	—	18	2	no	—
318	#41	—	18	4	no	—
319	#41	C₂×C₃×C₃⋊D₃	1	2	yes	—
320	C₂×Q₈	—	9	4	no	—
321	C₂×Q₈	—	9	2	no	—
322	C₂×Q₈	—	18	2	no	—
323	Q₁₆	—	9	4	no	—
324	Q₁₆	—	9	2	no	—
325	Q₁₆	—	9	2	no	—
326	Q₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
327	SD₁₆	—	9	4	no	—
328	SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	—
329	D₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
330	M₁₆	—	9	1	no	—
331	M₁₆	—	9	2	no	—
332	C₂×C₈	—	9	2	no	—
333	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
334	C₂²×C₃	—	2	8	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	4	no	—
337	C₂²×C₃	—	4	8	no	—
338	C₂²×C₃	—	9	2	no	—
339	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
340	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
341	C₂×D₃	—	3	8	no	—
342	C₃×C₄	—	2	8	no	—
343	C₃×C₄	—	2	2	no	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	—	4	8	no	—
347	C₃×C₄	—	9	2	no	—
348	C₃×C₄	—	18	4	no	—
349	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
350	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
351	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
352	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
353	Dic₃	—	3	8	no	—
354	Dic₃	—	6	16	no	—
355	C₃²	—	2	4	no	—
356	C₃²	#5771	1	4	yes	complemented
357	C₃²	C₃×#578	1	1	yes	characteristic, complemented
358	Q₈	—	9	1	no	—
359	Q₈	—	9	4	no	—
360	Q₈	—	18	4	no	—
361	Q₈	—	18	2	no	—
362	Q₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
363	D₄	—	2	2	no	—
364	D₄	—	9	2	no	—
365	D₄	—	9	1	no	—
366	D₄	—	18	4	no	—
367	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	9	2	no	—
370	C₂×C₄	—	18	4	no	—
371	C₂×C₄	—	18	4	no	—
372	C₂×C₄	—	18	2	no	—
373	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
374	C₈	—	9	2	no	—
375	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
376	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	4	no	—
380	C₂×C₃	—	4	4	no	—
381	C₂×C₃	—	4	8	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	—	8	8	no	—
384	C₂×C₃	—	18	2	no	—
385	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
386	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
387	D₃	—	6	8	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	9	2	no	—
390	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	9	2	no	—
393	C₄	—	18	4	no	—
394	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
395	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
396	C₃	—	2	4	no	—
397	C₃	C₃×#5771	1	4	yes	complemented
398	C₃	#10596242	1	1	yes	characteristic, direct product factor
399	C₂	—	2	1	no	—
400	C₂	—	4	2	no	—
401	C₂	—	18	2	no	—
402	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#135	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₃×#135	C₃⋊D₃
hypocenter	C₃²	C₃×#578
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₃×#64367	C₂	semidirect
2. C₃³×#135	C₂	semidirect
3. C₃×#64160	C₂	semidirect
4. C₃×Q₁₆×C₃⋊D₃	C₂	semidirect
5. C₃×#64124	C₂	semidirect
6. C₃×#64121	C₂	semidirect
7. C₂×C₃×#3746	C₂	semidirect
8. C₃×#64110	C₂	semidirect
9. #10596242	C₃	direct (N × H)
30. #64367	C₂×C₃	semidirect
33. C₃²×#135	D₃	semidirect
34. C₃²×#135	C₂×C₃	semidirect
35. #64160	C₂×C₃	semidirect
36. Q₁₆×C₃⋊D₃	C₂×C₃	semidirect
37. #64124	C₂×C₃	semidirect
38. #64121	C₂×C₃	semidirect
39. C₂×#3746	C₂×C₃	semidirect
40. #64110	C₂×C₃	semidirect
125. C₃×#135	C₃×D₃	semidirect
126. C₃×#135	C₃⋊D₃	semidirect
254. #135	C₃×C₃⋊D₃	semidirect
258. C₃³	#578	semidirect
356. C₃²	#5771	semidirect
357. C₃²	C₃×#578	semidirect
397. C₃	C₃×#5771	semidirect
398. C₃	#10596242	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#64367	2
C₃³×#135	2
C₃×#64160	2
C₃×Q₁₆×C₃⋊D₃	2
C₃×#64124	2
C₃×#64121	2
C₂×C₃×#3746	2
C₃×#64110	2
#10596242	3
C₃×#5771	3

Subgroups — C3×#10596242 #13179522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596242 #13179522