Subgroups — C₃×#10596050 #13179330

Order 1728.

1648 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64155	C₂	1	2	yes	maximal, complemented
3	C₃×#64105	C₂	1	4	yes	maximal, complemented
4	C₃×C₄⋊C₄×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
7	C₃×#64079	C₂	1	2	yes	maximal, complemented
8	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596050	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5579	—	3	4	no	maximal
11	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
14	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	—
15	C₂×C₃×#634	C₂²	1	2	yes	—
16	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃³×C₄²	C₂²	1	1	yes	characteristic
19	C₃³×C₄²	C₂²	1	2	yes	—
20	C₃×#3752	C₂²	1	2	yes	—
21	C₃×#3752	C₂²	1	4	yes	—
22	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
24	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
25	C₃×#3750	C₂²	1	4	yes	—
26	C₃×#3750	C₂²	1	4	yes	—
27	C₃²×C₄×Q₈	—	2	4	no	—
28	C₃²×C₄×Q₈	D₃	1	4	yes	complemented
29	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	#64155	C₂×C₃	1	2	yes	complemented
31	#64105	C₂×C₃	1	4	yes	complemented
32	C₄⋊C₄×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
33	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	2	yes	—
34	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
35	#64079	C₂×C₃	1	2	yes	complemented
36	#64078	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×#946	—	3	8	no	—
38	C₃×#896	—	3	16	no	—
39	C₃×D₃×C₄⋊C₄	—	3	8	no	—
40	C₃×C₄×D₁₂	—	3	8	no	—
41	C₃×C₄×D₁₂	—	3	4	no	—
42	C₃×#870	—	3	8	no	—
43	C₃×#869	—	3	4	no	—
44	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
45	C₃³×Q₈	—	2	2	no	—
46	C₂×C₃³×C₄	C₂³	1	2	yes	—
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
53	C₃×C₄⋊(C₃⋊D₃)	Q₈	1	4	yes	complemented
54	C₃×C₄×C₃⋊D₃	—	2	4	no	—
55	C₃×C₄×C₃⋊D₃	—	4	4	no	—
56	C₃×#634	—	4	2	no	—
57	C₃×#554	—	9	1	no	—
58	#5579	—	3	4	no	—
59	C₂×C₃²×Q₈	—	2	4	no	—
60	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
61	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
64	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	—
65	C₂×#634	C₂²×C₃	1	2	yes	—
66	C₂×C₃×D₁₂	—	3	4	no	—
67	C₂×C₃×C₄×D₃	—	3	8	no	—
68	C₂×C₃×C₄×D₃	—	3	16	no	—
69	C₂×C₃×Dic₆	—	3	8	no	—
70	C₃²×C₄⋊C₄	—	2	4	no	—
71	C₃²×C₄⋊C₄	—	2	8	no	—
72	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
73	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
74	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₃²×C₄²	—	2	4	no	—
77	C₃²×C₄²	—	2	8	no	—
78	C₃²×C₄²	C₂×D₃	1	4	yes	—
79	C₃²×C₄²	C₂×D₃	1	8	yes	—
80	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
81	C₃²×C₄²	C₂²×C₃	1	2	yes	—
82	#3752	C₂²×C₃	1	2	yes	—
83	#3752	C₂²×C₃	1	4	yes	—
84	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
85	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
86	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
87	#3750	C₂²×C₃	1	4	yes	—
88	#3750	C₂²×C₃	1	4	yes	—
89	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
91	C₃×C₄⋊Dic₃	—	3	8	no	—
92	C₃×C₄⋊Dic₃	—	3	8	no	—
93	C₃×C₄⋊Dic₃	—	3	4	no	—
94	C₃×Dic₃⋊C₄	—	3	16	no	—
95	C₃×Dic₃⋊C₄	—	3	16	no	—
96	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
97	C₂×C₃×C₃⋊D₃	—	2	2	no	—
98	C₂×C₃×C₃⋊D₃	—	2	2	no	—
99	C₂×C₃×C₃⋊D₃	C₂×Q₈	1	4	yes	—
100	C₃³×C₄	—	2	2	no	—
101	C₃³×C₄	—	2	1	no	—
102	C₃³×C₄	—	2	2	no	—
103	C₃³×C₄	C₂×Q₈	1	2	yes	—
104	C₃³×C₄	#41	1	2	yes	—
105	C₃×C₃⋊Dic₃	—	2	2	no	—
106	C₃×C₃⋊Dic₃	—	2	4	no	—
107	C₃×C₄⋊Q₈	—	9	1	no	—
108	C₃×#125	—	9	2	no	—
109	C₃×C₂²⋊Q₈	—	9	2	no	—
110	C₃×C₂²⋊Q₈	—	9	4	no	—
111	C₃×C₄×Q₈	—	2	4	no	—
112	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
113	C₃×C₄×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
114	C₃×C₄×D₄	—	9	2	no	—
115	C₃×C₄×D₄	—	9	1	no	—
116	C₂×C₃×C₄⋊C₄	—	9	2	no	—
117	#946	—	3	8	no	—
118	#896	—	3	16	no	—
119	D₃×C₄⋊C₄	—	3	8	no	—
120	C₄×D₁₂	—	3	8	no	—
121	C₄×D₁₂	—	3	4	no	—
122	#870	—	3	8	no	—
123	#869	—	3	4	no	—
124	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
125	C₂²×C₃×D₃	—	3	8	no	—
126	C₃²×Q₈	—	2	16	no	—
127	C₃²×Q₈	—	2	8	no	—
128	C₃²×Q₈	—	2	2	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	8	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	8	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
135	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
136	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
137	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
138	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
139	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
140	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
141	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
145	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
146	C₄⋊(C₃⋊D₃)	C₃×Q₈	1	4	yes	complemented
147	C₄×C₃⋊D₃	—	2	4	no	—
148	C₄×C₃⋊D₃	—	4	4	no	—
149	#634	—	4	2	no	—
150	C₂×C₃×Dic₃	—	3	8	no	—
151	C₂×C₃×Dic₃	—	3	16	no	—
152	C₃×D₁₂	—	3	16	no	—
153	C₃×C₄×D₃	—	6	16	no	—
154	C₃×C₄×D₃	—	12	16	no	—
155	C₃×Dic₆	—	12	8	no	—
156	#554	—	9	1	no	Sylow
157	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₃³	C₂×#41	1	1	yes	characteristic
159	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
160	C₃×C₃⋊D₃	—	2	4	no	—
161	C₂×C₃×Q₈	—	2	4	no	—
162	C₂×C₃×Q₈	—	9	2	no	—
163	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
164	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
165	C₂×C₃×D₄	—	9	1	no	—
166	C₂²×C₃×C₄	—	9	2	no	—
167	C₂²×C₃×C₄	—	9	4	no	—
168	C₂×D₁₂	—	3	4	no	—
169	C₂×C₄×D₃	—	3	8	no	—
170	C₂×C₄×D₃	—	3	16	no	—
171	C₂×Dic₆	—	3	8	no	—
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	2	8	no	—
174	C₃×C₄⋊C₄	—	9	4	no	—
175	C₃×C₄⋊C₄	—	9	4	no	—
176	C₃×C₄⋊C₄	—	9	2	no	—
177	C₃×C₄⋊C₄	—	9	1	no	—
178	C₃×C₄⋊C₄	—	9	2	no	—
179	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
180	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
181	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
183	C₃×C₂²⋊C₄	—	9	2	no	—
184	C₃×C₂²⋊C₄	—	9	4	no	—
185	C₃×C₄²	—	2	8	no	—
186	C₃×C₄²	—	2	4	no	—
187	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
188	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
189	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	—
190	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
191	(C₂×D₃)⋊C₄	—	3	8	no	—
192	(C₂×D₃)⋊C₄	—	3	16	no	—
193	C₄⋊Dic₃	—	3	8	no	—
194	C₄⋊Dic₃	—	3	8	no	—
195	C₄⋊Dic₃	—	3	4	no	—
196	Dic₃⋊C₄	—	3	16	no	—
197	Dic₃⋊C₄	—	3	16	no	—
198	C₂²×C₃²	—	2	4	no	—
199	C₂²×C₃²	C₂³×D₃	1	4	yes	—
200	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
201	C₂×C₃⋊D₃	—	2	2	no	—
202	C₂×C₃⋊D₃	—	2	2	no	—
203	C₂×C₃⋊D₃	C₂×C₃×Q₈	1	4	yes	—
204	C₂×C₃×D₃	—	3	16	no	—
205	C₂×C₃×D₃	—	6	8	no	—
206	C₂×C₃×D₃	—	6	8	no	—
207	C₃²×C₄	—	2	16	no	—
208	C₃²×C₄	—	2	8	no	—
209	C₃²×C₄	—	2	2	no	—
210	C₃²×C₄	—	2	1	no	—
211	C₃²×C₄	—	2	2	no	—
212	C₃²×C₄	—	2	8	no	—
213	C₃²×C₄	—	2	8	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	2	8	no	—
216	C₃²×C₄	—	4	4	no	—
217	C₃²×C₄	—	4	8	no	—
218	C₃²×C₄	#235	1	8	yes	—
219	C₃²×C₄	D₃×Q₈	1	8	yes	—
220	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
221	C₃²×C₄	C₃×#41	1	2	yes	—
222	C₃⋊Dic₃	—	2	2	no	—
223	C₃⋊Dic₃	—	2	4	no	—
224	C₃×Dic₃	—	6	8	no	—
225	C₃×Dic₃	—	6	16	no	—
226	C₄⋊Q₈	—	9	1	no	—
227	#125	—	9	2	no	—
228	C₂²⋊Q₈	—	9	2	no	—
229	C₂²⋊Q₈	—	9	4	no	—
230	C₄×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
231	C₄×D₄	—	9	2	no	—
232	C₄×D₄	—	9	1	no	—
233	C₂×C₄⋊C₄	—	9	2	no	—
234	C₃³	#554	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	9	2	no	—
236	C₂²×D₃	—	3	8	no	—
237	C₃×Q₈	—	2	16	no	—
238	C₃×Q₈	—	2	8	no	—
239	C₃×Q₈	—	2	2	no	—
240	C₃×Q₈	—	36	2	no	—
241	C₃×D₄	—	9	4	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	8	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	9	2	no	—
248	C₂×C₃×C₄	—	9	4	no	—
249	C₂×C₃×C₄	—	18	4	no	—
250	C₂×C₃×C₄	—	36	4	no	—
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
256	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
257	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
259	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
261	C₂×Dic₃	—	3	8	no	—
262	C₂×Dic₃	—	3	16	no	—
263	D₁₂	—	3	16	no	—
264	C₄×D₃	—	6	16	no	—
265	C₄×D₃	—	12	16	no	—
266	Dic₆	—	12	8	no	—
267	C₂×C₃²	—	2	4	no	—
268	C₂×C₃²	—	2	4	no	—
269	C₂×C₃²	—	2	4	no	—
270	C₂×C₃²	C₂×#235	1	4	yes	—
271	C₂×C₃²	C₂×D₃×Q₈	1	4	yes	—
272	C₂×C₃²	#1009	1	4	yes	—
273	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
274	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
275	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
276	C₃⋊D₃	—	2	4	no	—
277	C₃×D₃	—	6	16	no	—
278	C₂×Q₈	—	9	2	no	—
279	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
280	C₂×D₄	—	9	1	no	—
281	C₂²×C₄	—	9	2	no	—
282	C₂²×C₄	—	9	4	no	—
283	C₄⋊C₄	—	9	4	no	—
284	C₄⋊C₄	—	9	2	no	—
285	C₄⋊C₄	—	9	1	no	—
286	C₄⋊C₄	—	9	2	no	—
287	C₄⋊C₄	—	9	4	no	—
288	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
289	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
290	C₂²⋊C₄	—	9	2	no	—
291	C₂²⋊C₄	—	9	4	no	—
292	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	—
293	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
294	C₂²×C₃	—	2	4	no	—
295	C₂²×C₃	—	9	4	no	—
296	C₂²×C₃	—	18	2	no	—
297	C₂²×C₃	—	18	2	no	—
298	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
299	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
300	C₂×D₃	—	3	16	no	—
301	C₂×D₃	—	6	8	no	—
302	C₂×D₃	—	6	8	no	—
303	C₃×C₄	—	2	16	no	—
304	C₃×C₄	—	2	8	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	2	8	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	8	no	—
311	C₃×C₄	—	2	8	no	—
312	C₃×C₄	—	4	8	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	—	18	2	no	—
315	C₃×C₄	—	18	4	no	—
316	C₃×C₄	C₃×#235	1	8	yes	—
317	C₃×C₄	C₃×D₃×Q₈	1	8	yes	—
318	C₃×C₄	#3828	1	2	yes	—
319	C₃×C₄	Q₈×C₃⋊D₃	1	2	yes	—
320	Dic₃	—	6	8	no	—
321	Dic₃	—	6	16	no	—
322	C₃²	—	2	4	no	—
323	C₃²	#5579	1	4	yes	complemented
324	C₃²	C₃×#554	1	1	yes	characteristic, complemented
325	C₂³	—	9	2	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	36	2	no	—
328	D₄	—	9	4	no	—
329	C₂×C₄	—	9	2	no	—
330	C₂×C₄	—	9	4	no	—
331	C₂×C₄	—	18	4	no	—
332	C₂×C₄	—	36	4	no	—
333	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
334	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
336	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
338	C₂×C₃	—	2	4	no	—
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	2	4	no	—
341	C₂×C₃	—	18	4	no	—
342	C₂×C₃	C₂×C₃×#235	1	4	yes	—
343	C₂×C₃	C₂×C₃×D₃×Q₈	1	4	yes	—
344	C₂×C₃	C₃×#1009	1	4	yes	—
345	C₂×C₃	C₂×#3828	1	1	yes	characteristic
346	C₂×C₃	C₂×Q₈×C₃⋊D₃	1	1	yes	characteristic
347	C₂×C₃	#64366	1	1	yes	characteristic
348	D₃	—	6	16	no	—
349	C₂²	—	9	4	no	—
350	C₂²	—	18	2	no	—
351	C₂²	—	18	2	no	—
352	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	18	2	no	—
357	C₄	—	18	4	no	—
358	C₄	C₃×#3828	1	2	yes	—
359	C₄	C₃×Q₈×C₃⋊D₃	1	2	yes	—
360	C₃	—	2	4	no	—
361	C₃	C₃×#5579	1	4	yes	complemented
362	C₃	#10596050	1	1	yes	characteristic, direct product factor
363	C₂	—	18	4	no	—
364	C₂	C₂×C₃×#3828	1	1	yes	characteristic
365	C₂	C₂×C₃×Q₈×C₃⋊D₃	1	1	yes	characteristic
366	C₂	C₃×#64366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²
hypercenter	C₃×C₄×Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×#554
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
2. C₃×#64155	C₂	semidirect
3. C₃×#64105	C₂	semidirect
4. C₃×C₄⋊C₄×C₃⋊D₃	C₂	semidirect
7. C₃×#64079	C₂	semidirect
8. C₃×#64078	C₂	semidirect
9. #10596050	C₃	direct (N × H)
28. C₃²×C₄×Q₈	D₃	semidirect
29. C₃²×C₄×Q₈	C₂×C₃	semidirect
30. #64155	C₂×C₃	semidirect
31. #64105	C₂×C₃	semidirect
32. C₄⋊C₄×C₃⋊D₃	C₂×C₃	semidirect
35. #64079	C₂×C₃	semidirect
36. #64078	C₂×C₃	semidirect
53. C₃×C₄⋊(C₃⋊D₃)	Q₈	semidirect
112. C₃×C₄×Q₈	C₃×D₃	semidirect
113. C₃×C₄×Q₈	C₃⋊D₃	semidirect
146. C₄⋊(C₃⋊D₃)	C₃×Q₈	semidirect
230. C₄×Q₈	C₃×C₃⋊D₃	semidirect
234. C₃³	#554	semidirect
323. C₃²	#5579	semidirect
324. C₃²	C₃×#554	semidirect
361. C₃	C₃×#5579	semidirect
362. C₃	#10596050	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×Q₈	2
C₃×#64155	2
C₃×#64105	2
C₃×C₄⋊C₄×C₃⋊D₃	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64079	2
C₃×#64078	2
#10596050	3
C₃×#5579	3

Subgroups — C3×#10596050 #13179330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596050 #13179330