Subgroups — C₃²×#5683 #13179060

Order 1728.

1864 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#947	C₂	1	2	yes	maximal, complemented
3	C₃²×#937	C₂	1	2	yes	maximal, complemented
4	C₃²×#885	C₂	1	4	yes	maximal, complemented
5	C₃²×#882	C₂	1	4	yes	maximal, complemented
6	C₃²×#875	C₂	1	2	yes	maximal, complemented
7	C₃²×H(3,𝔽₄)	—	3	1	no	maximal
8	C₃×#5683	C₃	1	4	yes	maximal, direct product factor
9	C₂³×C₃²×D₃	C₂²	1	2	yes	complemented
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃²×#67	C₂²	1	4	yes	—
13	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
14	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
15	C₂×C₃²×Dic₆	C₂²	1	2	yes	complemented
16	C₃³×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
18	C₃²×#217	C₂²	1	2	yes	complemented
19	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
20	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
21	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
22	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
23	C₃²×#124	—	2	4	no	—
24	C₃²×#124	—	3	2	no	—
25	C₃²×#124	—	3	4	no	—
26	C₃²×#124	—	3	2	no	—
27	C₃²×#124	D₃	1	1	yes	characteristic, complemented
28	C₃²×#124	C₂×C₃	1	4	yes	complemented
29	C₃²×#120	—	3	2	no	—
30	C₃²×#120	—	3	4	no	—
31	C₃×#947	C₂×C₃	1	8	yes	complemented
32	C₃×#937	C₂×C₃	1	8	yes	complemented
33	C₃×#885	C₂×C₃	1	16	yes	complemented
34	C₃×#882	C₂×C₃	1	16	yes	complemented
35	C₃×#875	C₂×C₃	1	8	yes	complemented
36	C₂³×C₃³	C₂³	1	2	yes	—
37	C₂²×C₃²×D₃	—	4	2	no	—
38	C₂²×C₃²×D₃	—	4	4	no	—
39	C₂²×C₃²×D₃	C₂³	1	4	yes	—
40	C₃³×Q₈	—	4	1	no	—
41	C₃³×D₄	—	4	1	no	—
42	C₂×C₃³×C₄	C₂³	1	2	yes	—
43	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
44	C₂×C₃³×C₄	C₂³	1	2	yes	—
45	C₃²×#67	—	4	4	no	—
46	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
47	C₃²×D₁₂	—	4	2	no	—
48	C₃²×D₁₂	—	4	2	no	—
49	C₃²×Dic₆	—	4	2	no	—
50	C₃×H(3,𝔽₄)	—	3	4	no	—
51	#5683	C₃²	1	1	yes	characteristic, direct product factor
52	C₂⁴×C₃²	—	3	2	no	—
53	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	complemented
54	C₂×C₃²×Q₈	—	2	4	no	—
55	C₂×C₃²×Q₈	—	3	2	no	—
56	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
57	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
58	C₂×C₃²×D₄	—	2	4	no	—
59	C₂×C₃²×D₄	—	3	4	no	—
60	C₂×C₃²×D₄	—	3	2	no	—
61	C₂×C₃²×D₄	—	3	2	no	—
62	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
64	C₂×C₃×#67	C₂²×C₃	1	16	yes	—
65	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
67	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	complemented
68	C₃²×C₂²⋊C₄	—	2	16	no	—
69	C₃²×C₂²⋊C₄	—	3	2	no	—
70	C₃²×C₂²⋊C₄	—	3	4	no	—
71	C₃²×C₂²⋊C₄	—	3	4	no	—
72	C₃²×C₂²⋊C₄	—	3	4	no	—
73	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
74	C₃²×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
75	C₃²×C₄²	—	2	4	no	—
76	C₃²×C₄²	—	3	2	no	—
77	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
78	C₃²×C₄²	C₂²×C₃	1	4	yes	complemented
79	C₃×#217	C₂²×C₃	1	8	yes	complemented
80	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
81	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
82	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
83	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
84	C₂²×C₃³	—	2	4	no	—
85	C₂²×C₃³	—	2	2	no	—
86	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
87	C₂×C₃²×D₃	—	2	4	no	—
88	C₂×C₃²×D₃	—	2	4	no	—
89	C₂×C₃²×D₃	—	2	4	no	—
90	C₂×C₃²×D₃	—	4	8	no	—
91	C₃³×C₄	—	2	1	no	—
92	C₃³×C₄	—	2	2	no	—
93	C₃³×C₄	—	2	2	no	—
94	C₃²×Dic₃	—	2	4	no	—
95	C₃×#124	—	2	4	no	—
96	C₃×#124	—	3	8	no	—
97	C₃×#124	—	3	16	no	—
98	C₃×#124	—	3	8	no	—
99	C₃×#124	C₃×D₃	1	4	yes	complemented
100	C₃×#124	C₂×C₃²	1	1	yes	characteristic, complemented
101	C₃×#120	—	3	8	no	—
102	C₃×#120	—	3	16	no	—
103	#947	C₂×C₃²	1	2	yes	complemented
104	#937	C₂×C₃²	1	2	yes	complemented
105	#885	C₂×C₃²	1	4	yes	complemented
106	#882	C₂×C₃²	1	4	yes	complemented
107	#875	C₂×C₃²	1	2	yes	complemented
108	C₂³×C₃²	—	2	8	no	—
109	C₂³×C₃²	—	3	4	no	—
110	C₂³×C₃²	—	12	2	no	—
111	C₂³×C₃²	—	12	4	no	—
112	C₂³×C₃²	C₂²×D₃	1	2	yes	—
113	C₂³×C₃²	C₂³×C₃	1	8	yes	—
114	C₂²×C₃×D₃	—	4	8	no	—
115	C₂²×C₃×D₃	—	4	16	no	—
116	C₂²×C₃×D₃	C₂³×C₃	1	16	yes	—
117	C₃²×Q₈	—	4	1	no	—
118	C₃²×Q₈	—	4	4	no	—
119	C₃²×Q₈	—	4	8	no	—
120	C₃²×Q₈	—	12	2	no	—
121	C₃²×D₄	—	4	1	no	—
122	C₃²×D₄	—	4	4	no	—
123	C₃²×D₄	—	4	8	no	—
124	C₃²×D₄	—	12	2	no	—
125	C₃²×D₄	—	12	2	no	—
126	C₃²×D₄	—	12	4	no	—
127	C₂×C₃²×C₄	—	2	4	no	—
128	C₂×C₃²×C₄	—	2	8	no	—
129	C₂×C₃²×C₄	—	2	8	no	—
130	C₂×C₃²×C₄	—	3	4	no	—
131	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
132	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
134	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
135	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
136	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
137	C₃×#67	—	4	16	no	—
138	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
139	C₃×D₁₂	—	4	8	no	—
140	C₃×D₁₂	—	4	8	no	—
141	C₃×Dic₆	—	4	8	no	—
142	H(3,𝔽₄)	—	3	1	no	Sylow
143	C₂×C₃³	—	4	2	no	—
144	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
146	C₃²×D₃	—	4	4	no	—
147	C₂⁴×C₃	—	3	8	no	—
148	C₂³×D₃	C₂²×C₃²	1	2	yes	complemented
149	C₂×C₃×Q₈	—	2	4	no	—
150	C₂×C₃×Q₈	—	3	8	no	—
151	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
152	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
153	C₂×C₃×D₄	—	2	4	no	—
154	C₂×C₃×D₄	—	3	16	no	—
155	C₂×C₃×D₄	—	3	8	no	—
156	C₂×C₃×D₄	—	3	8	no	—
157	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
158	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
159	C₂×#67	C₂²×C₃²	1	4	yes	—
160	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
161	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
162	C₂×Dic₆	C₂²×C₃²	1	2	yes	complemented
163	C₃×C₂²⋊C₄	—	2	16	no	—
164	C₃×C₂²⋊C₄	—	3	8	no	—
165	C₃×C₂²⋊C₄	—	3	16	no	—
166	C₃×C₂²⋊C₄	—	3	16	no	—
167	C₃×C₂²⋊C₄	—	3	16	no	—
168	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	16	yes	complemented
169	C₃×C₂²⋊C₄	C₂²×C₃²	1	4	yes	complemented
170	C₃×C₄²	—	2	4	no	—
171	C₃×C₄²	—	3	8	no	—
172	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
173	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
174	#217	C₂²×C₃²	1	2	yes	complemented
175	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
176	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
177	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
178	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
179	C₂²×C₃²	—	2	2	no	—
180	C₂²×C₃²	—	2	4	no	—
181	C₂²×C₃²	—	2	4	no	—
182	C₂²×C₃²	—	2	16	no	—
183	C₂²×C₃²	—	2	8	no	—
184	C₂²×C₃²	—	4	8	no	—
185	C₂²×C₃²	—	4	16	no	—
186	C₂²×C₃²	—	6	4	no	—
187	C₂²×C₃²	—	6	4	no	—
188	C₂²×C₃²	—	6	4	no	—
189	C₂²×C₃²	—	12	8	no	—
190	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
191	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
192	C₂×C₃×D₃	—	2	16	no	—
193	C₂×C₃×D₃	—	2	16	no	—
194	C₂×C₃×D₃	—	2	16	no	—
195	C₂×C₃×D₃	—	4	32	no	—
196	C₃²×C₄	—	2	8	no	—
197	C₃²×C₄	—	2	1	no	—
198	C₃²×C₄	—	2	2	no	—
199	C₃²×C₄	—	2	2	no	—
200	C₃²×C₄	—	2	4	no	—
201	C₃²×C₄	—	2	8	no	—
202	C₃²×C₄	—	2	8	no	—
203	C₃²×C₄	—	4	8	no	—
204	C₃²×C₄	—	4	8	no	—
205	C₃²×C₄	—	6	4	no	—
206	C₃×Dic₃	—	2	16	no	—
207	#124	—	3	2	no	—
208	#124	—	3	4	no	—
209	#124	—	3	2	no	—
210	#124	C₃²×D₃	1	1	yes	characteristic, complemented
211	#120	—	3	2	no	—
212	#120	—	3	4	no	—
213	C₃³	H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
214	C₂³×C₃	—	2	8	no	—
215	C₂³×C₃	—	3	16	no	—
216	C₂³×C₃	—	12	8	no	—
217	C₂³×C₃	—	12	16	no	—
218	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
219	C₂³×C₃	C₂³×C₃²	1	2	yes	—
220	C₂²×D₃	—	4	2	no	—
221	C₂²×D₃	—	4	4	no	—
222	C₂²×D₃	C₂³×C₃²	1	4	yes	—
223	C₃×Q₈	—	4	4	no	—
224	C₃×Q₈	—	4	1	no	—
225	C₃×Q₈	—	4	8	no	—
226	C₃×Q₈	—	12	8	no	—
227	C₃×D₄	—	4	4	no	—
228	C₃×D₄	—	4	1	no	—
229	C₃×D₄	—	4	8	no	—
230	C₃×D₄	—	12	8	no	—
231	C₃×D₄	—	12	8	no	—
232	C₃×D₄	—	12	16	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	8	no	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	3	16	no	—
237	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
238	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
239	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
240	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
241	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
243	#67	—	4	4	no	—
244	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
245	D₁₂	—	4	2	no	—
246	D₁₂	—	4	2	no	—
247	Dic₆	—	4	2	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	—	2	8	no	—
250	C₂×C₃²	—	4	2	no	—
251	C₂×C₃²	—	4	8	no	—
252	C₂×C₃²	—	8	8	no	—
253	C₂×C₃²	—	12	4	no	—
254	C₂×C₃²	#1004	1	1	yes	characteristic
255	C₂×C₃²	#1009	1	2	yes	—
256	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
257	C₂×C₃²	C₃×H(5,𝔽₂)	1	8	yes	—
258	C₃×D₃	—	4	16	no	—
259	C₂⁴	—	3	2	no	—
260	C₂×Q₈	—	3	2	no	—
261	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
262	C₂×D₄	—	3	4	no	—
263	C₂×D₄	—	3	2	no	—
264	C₂×D₄	—	3	2	no	—
265	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
266	C₂²⋊C₄	—	3	2	no	—
267	C₂²⋊C₄	—	3	4	no	—
268	C₂²⋊C₄	—	3	4	no	—
269	C₂²⋊C₄	—	3	4	no	—
270	C₂²⋊C₄	C₂×C₃²×D₃	1	4	yes	complemented
271	C₄²	—	3	2	no	—
272	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
273	C₂²×C₃	—	2	8	no	—
274	C₂²×C₃	—	2	16	no	—
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	4	8	no	—
279	C₂²×C₃	—	4	16	no	—
280	C₂²×C₃	—	6	16	no	—
281	C₂²×C₃	—	6	16	no	—
282	C₂²×C₃	—	6	16	no	—
283	C₂²×C₃	—	12	32	no	—
284	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
285	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
286	C₂×D₃	—	2	4	no	—
287	C₂×D₃	—	2	4	no	—
288	C₂×D₃	—	2	4	no	—
289	C₂×D₃	—	4	8	no	—
290	C₃×C₄	—	2	8	no	—
291	C₃×C₄	—	2	4	no	—
292	C₃×C₄	—	2	8	no	—
293	C₃×C₄	—	2	8	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	4	8	no	—
298	C₃×C₄	—	4	8	no	—
299	C₃×C₄	—	6	16	no	—
300	Dic₃	—	2	4	no	—
301	C₃²	—	2	4	no	—
302	C₃²	#5683	1	1	yes	characteristic, direct product factor
303	C₃²	C₃×H(3,𝔽₄)	1	4	yes	complemented
304	C₂³	—	3	4	no	—
305	C₂³	—	12	2	no	—
306	C₂³	—	12	4	no	—
307	C₂³	C₂²×C₃²×D₃	1	2	yes	—
308	Q₈	—	4	1	no	—
309	Q₈	—	12	2	no	—
310	D₄	—	4	1	no	—
311	D₄	—	12	2	no	—
312	D₄	—	12	2	no	—
313	D₄	—	12	4	no	—
314	C₂×C₄	—	3	4	no	—
315	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
316	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
318	C₂×C₃	—	2	4	no	—
319	C₂×C₃	—	2	8	no	—
320	C₂×C₃	—	4	2	no	—
321	C₂×C₃	—	4	8	no	—
322	C₂×C₃	—	8	8	no	—
323	C₂×C₃	—	12	16	no	—
324	C₂×C₃	C₃×#1004	1	4	yes	—
325	C₂×C₃	C₃×#1009	1	8	yes	—
326	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂×C₃	C₃²×H(5,𝔽₂)	1	2	yes	—
328	D₃	—	4	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	6	4	no	—
332	C₂²	—	6	4	no	—
333	C₂²	—	6	4	no	—
334	C₂²	—	12	8	no	—
335	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	6	4	no	—
340	C₃	—	2	4	no	—
341	C₃	C₃×#5683	1	4	yes	direct product factor
342	C₃	C₃²×H(3,𝔽₄)	1	1	yes	characteristic, complemented
343	C₂	—	4	2	no	—
344	C₂	—	12	4	no	—
345	C₂	C₃²×#1004	1	1	yes	characteristic
346	C₂	C₃²×#1009	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×#124	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃²×#124	D₃
hypocenter	C₃	C₃²×H(3,𝔽₄)
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#124

Complements

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

N	H ≅ G/N	type
1. C₃³×#124	C₂	semidirect
2. C₃²×#947	C₂	semidirect
3. C₃²×#937	C₂	semidirect
4. C₃²×#885	C₂	semidirect
5. C₃²×#882	C₂	semidirect
6. C₃²×#875	C₂	semidirect
8. C₃×#5683	C₃	direct (N × H)
9. C₂³×C₃²×D₃	C₂²	semidirect
10. C₂×C₃³×Q₈	C₂²	semidirect
15. C₂×C₃²×Dic₆	C₂²	semidirect
16. C₃³×C₂²⋊C₄	C₂²	semidirect
17. C₃³×C₄²	C₂²	semidirect
18. C₃²×#217	C₂²	semidirect
19. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
20. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
22. C₃²×C₄×Dic₃	C₂²	semidirect
27. C₃²×#124	D₃	semidirect
28. C₃²×#124	C₂×C₃	semidirect
31. C₃×#947	C₂×C₃	semidirect
32. C₃×#937	C₂×C₃	semidirect
33. C₃×#885	C₂×C₃	semidirect
34. C₃×#882	C₂×C₃	semidirect
35. C₃×#875	C₂×C₃	semidirect
51. #5683	C₃²	direct (N × H)
53. C₂³×C₃×D₃	C₂²×C₃	semidirect
56. C₂×C₃²×Q₈	C₂×D₃	semidirect
57. C₂×C₃²×Q₈	C₂²×C₃	semidirect
67. C₂×C₃×Dic₆	C₂²×C₃	semidirect
73. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
74. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
77. C₃²×C₄²	C₂×D₃	semidirect
78. C₃²×C₄²	C₂²×C₃	semidirect
79. C₃×#217	C₂²×C₃	semidirect
80. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
81. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
82. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
83. C₃×C₄×Dic₃	C₂²×C₃	semidirect
99. C₃×#124	C₃×D₃	semidirect
100. C₃×#124	C₂×C₃²	semidirect
103. #947	C₂×C₃²	semidirect
104. #937	C₂×C₃²	semidirect
105. #885	C₂×C₃²	semidirect
106. #882	C₂×C₃²	semidirect
107. #875	C₂×C₃²	semidirect
148. C₂³×D₃	C₂²×C₃²	semidirect
151. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
152. C₂×C₃×Q₈	C₂²×C₃²	semidirect
162. C₂×Dic₆	C₂²×C₃²	semidirect
168. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
169. C₃×C₂²⋊C₄	C₂²×C₃²	semidirect
172. C₃×C₄²	C₂×C₃×D₃	semidirect
173. C₃×C₄²	C₂²×C₃²	semidirect
174. #217	C₂²×C₃²	semidirect
175. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
176. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
177. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
178. C₄×Dic₃	C₂²×C₃²	semidirect
210. #124	C₃²×D₃	semidirect
213. C₃³	H(3,𝔽₄)	semidirect
261. C₂×Q₈	C₂×C₃²×D₃	semidirect
270. C₂²⋊C₄	C₂×C₃²×D₃	semidirect
272. C₄²	C₂×C₃²×D₃	semidirect
302. C₃²	#5683	direct (N × H)
303. C₃²	C₃×H(3,𝔽₄)	semidirect
341. C₃	C₃×#5683	direct (N × H)
342. C₃	C₃²×H(3,𝔽₄)	semidirect

Maximal subgroups

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

subgroup	index
C₃³×#124	2
C₃²×#947	2
C₃²×#937	2
C₃²×#885	2
C₃²×#882	2
C₃²×#875	2
C₃²×H(3,𝔽₄)	3
C₃×#5683	3

Subgroups — C32×#5683 #13179060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5683 #13179060