Subgroups — #10592536⋊C₃ #13142045

Order 1728.

479 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3743⋊C₃	C₂	1	2	yes	maximal
2	C₄²×(C₃⋊D₃)⋊C₃	C₂	1	1	yes	maximal, characteristic
3	H(3,𝔽₃)×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#63641⋊C₃	C₂	1	2	yes	maximal, complemented
5	C₄⋊((C₃⋊(C₃⋊C₈))⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	#10592536	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×#4837	—	3	1	no	maximal
8	C₂×C₄×(C₃⋊D₃)⋊C₃	C₄	1	1	yes	characteristic
9	C₂×C₄×(C₃⋊D₃)⋊C₃	C₄	1	1	yes	characteristic
10	C₂×C₄×(C₃⋊D₃)⋊C₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×H(3,𝔽₃)	C₂²	1	2	yes	—
12	C₄²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
13	C₄×(C₃⋊Dic₃)⋊C₃	C₄	1	1	yes	characteristic
14	C₄×(C₃⋊Dic₃)⋊C₃	C₄	1	1	yes	characteristic
15	C₄×(C₃⋊Dic₃)⋊C₃	C₂²	1	1	yes	characteristic
16	C₂×(C₃⋊(C₃⋊C₈))⋊C₃	C₂²	1	2	yes	—
17	#3743⋊C₃	—	2	4	no	—
18	C₂×#3743	C₂×C₃	1	2	yes	—
19	C₄²×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
21	C₃×C₄²×D₃	—	3	1	no	—
22	C₃²×C₄⋊C₈	—	2	1	no	—
23	C₃²×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
24	C₃²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
25	#63641	C₂×C₃	1	2	yes	complemented
26	C₄⋊(C₃⋊(C₃⋊C₈))	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×Dic₃⋊C₈	—	3	2	no	—
28	C₃×C₄⋊(C₃⋊C₈)	—	3	1	no	—
29	C₂²×(C₃⋊D₃)⋊C₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
33	C₂×(C₃⋊Dic₃)⋊C₃	C₂×C₄	1	1	yes	characteristic
34	C₂×(C₃⋊Dic₃)⋊C₃	C₂×C₄	1	1	yes	characteristic
35	C₂×(C₃⋊Dic₃)⋊C₃	C₂×C₄	1	1	yes	characteristic
36	C₄×(C₃⋊D₃)⋊C₃	—	2	2	no	—
37	C₄×(C₃⋊D₃)⋊C₃	—	2	2	no	—
38	C₄×(C₃⋊D₃)⋊C₃	D₄	1	2	yes	—
39	C₄×(C₃⋊D₃)⋊C₃	Q₈	1	2	yes	—
40	C₈×H(3,𝔽₃)	—	2	2	no	—
41	(C₃⋊(C₃⋊C₈))⋊C₃	—	2	2	no	—
42	C₃×#423	—	9	1	no	—
43	#4837	—	3	1	no	—
44	#4837	—	9	1	no	—
45	C₂×C₄×C₃⋊D₃	C₃×C₄	1	1	yes	characteristic
46	C₂×C₄×C₃⋊D₃	C₃×C₄	1	1	yes	characteristic
47	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₃×C₄×D₃	—	3	1	no	—
49	C₂×C₃×C₄×D₃	—	3	1	no	—
50	C₂×C₃×C₄×D₃	—	3	1	no	—
51	C₂×C₃²×C₈	—	2	2	no	—
52	C₂×C₃²×C₈	C₂×D₃	1	2	yes	—
53	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	—
54	C₃²×C₄²	—	2	1	no	—
55	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
56	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
57	C₄×C₃⋊Dic₃	C₃×C₄	1	1	yes	characteristic
58	C₄×C₃⋊Dic₃	C₃×C₄	1	1	yes	characteristic
59	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
61	#3743	—	2	4	no	—
62	C₃×C₄×Dic₃	—	3	1	no	—
63	C₃×C₄×Dic₃	—	3	1	no	—
64	C₃×C₄×Dic₃	—	3	1	no	—
65	C₂×C₃×C₃⋊C₈	—	3	2	no	—
66	C₃×ΓL(1,𝔽₂₅)	—	6	4	no	—
67	C₂²×H(3,𝔽₃)	C₂²×C₄	1	1	yes	characteristic
68	C₂×(C₃⋊D₃)⋊C₃	—	2	1	no	—
69	C₂×(C₃⋊D₃)⋊C₃	—	2	1	no	—
70	C₂×(C₃⋊D₃)⋊C₃	C₄⋊C₄	1	2	yes	—
71	C₄×H(3,𝔽₃)	—	2	1	no	—
72	C₄×H(3,𝔽₃)	M₁₆	1	2	yes	complemented
73	C₄×H(3,𝔽₃)	C₂×D₄	1	1	yes	characteristic
74	C₄×H(3,𝔽₃)	C₂×Q₈	1	1	yes	characteristic
75	(C₃⋊Dic₃)⋊C₃	—	2	1	no	—
76	(C₃⋊Dic₃)⋊C₃	C₄⋊C₄	1	2	yes	—
77	(C₃⋊Dic₃)⋊C₃	M₁₆	1	2	yes	complemented
78	C₂×C₃×M₁₆	—	9	2	no	—
79	C₂×C₃×C₄²	—	9	1	no	—
80	C₂×ΓL(1,𝔽₂₅)	—	3	2	no	—
81	C₂×ΓL(1,𝔽₂₅)	—	9	2	no	—
82	C₄²×D₃	—	3	1	no	—
83	C₄²×D₃	—	9	1	no	—
84	C₃×C₄⋊C₈	—	3	1	no	—
85	C₃×C₄⋊C₈	—	3	1	no	—
86	C₃×C₄⋊C₈	—	6	1	no	—
87	C₃×C₄⋊C₈	—	9	1	no	—
88	C₃×C₄⋊C₈	—	9	2	no	—
89	C₃×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic
90	Dic₃⋊C₈	—	3	2	no	—
91	Dic₃⋊C₈	—	9	2	no	—
92	C₄⋊(C₃⋊C₈)	—	3	1	no	—
93	C₄⋊(C₃⋊C₈)	—	9	1	no	—
94	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	3	1	no	—
96	C₂×C₃²×C₄	—	2	1	no	—
97	C₂×C₃²×C₄	—	2	1	no	—
98	C₂×C₃²×C₄	—	2	1	no	—
99	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
105	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
106	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
107	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
108	C₄×C₃⋊D₃	—	2	2	no	—
109	C₄×C₃⋊D₃	—	2	2	no	—
110	C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
111	C₄×C₃⋊D₃	C₃×Q₈	1	2	yes	—
112	C₂×C₃×Dic₃	—	3	1	no	—
113	C₂×C₃×Dic₃	—	3	1	no	—
114	C₂×C₃×Dic₃	—	3	1	no	—
115	C₃×C₄×D₃	—	3	2	no	—
116	C₃×C₄×D₃	—	3	2	no	—
117	C₃×C₄×D₃	—	6	2	no	—
118	C₃×C₄×D₃	—	6	2	no	—
119	C₃²×C₈	—	2	2	no	—
120	C₃²×C₈	—	2	2	no	—
121	C₃²×C₈	—	4	2	no	—
122	C₃⋊(C₃⋊C₈)	—	2	2	no	—
123	C₃×C₃⋊C₈	—	6	2	no	—
124	#423	—	9	1	no	Sylow
125	C₂×H(3,𝔽₃)	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×H(3,𝔽₃)	C₂×M₁₆	1	1	yes	characteristic
127	C₂×H(3,𝔽₃)	C₂×M₁₆	1	1	yes	characteristic
128	(C₃⋊D₃)⋊C₃	—	2	2	no	—
129	C₂²×C₃×C₄	—	9	1	no	—
130	C₂²×C₃×C₄	—	9	1	no	—
131	C₂²×C₃×C₄	—	9	1	no	—
132	C₂×C₄×D₃	—	3	1	no	—
133	C₂×C₄×D₃	—	3	1	no	—
134	C₂×C₄×D₃	—	3	1	no	—
135	C₂×C₄×D₃	—	9	1	no	—
136	C₂×C₄×D₃	—	9	1	no	—
137	C₂×C₄×D₃	—	9	1	no	—
138	C₃×M₁₆	—	18	4	no	—
139	C₂×C₃×C₈	—	3	2	no	—
140	C₂×C₃×C₈	—	3	2	no	—
141	C₂×C₃×C₈	—	6	2	no	—
142	C₂×C₃×C₈	—	9	2	no	—
143	C₂×C₃×C₈	C₂×C₃×D₃	1	2	yes	—
144	C₃×C₄²	—	3	1	no	—
145	C₃×C₄²	—	3	1	no	—
146	C₃×C₄²	—	6	1	no	—
147	C₃×C₄²	—	9	1	no	—
148	C₃×C₄²	—	9	1	no	—
149	C₃×C₄²	—	9	1	no	—
150	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
151	C₄×Dic₃	—	3	1	no	—
152	C₄×Dic₃	—	3	1	no	—
153	C₄×Dic₃	—	3	1	no	—
154	C₄×Dic₃	—	9	1	no	—
155	C₄×Dic₃	—	9	1	no	—
156	C₄×Dic₃	—	9	1	no	—
157	C₂×C₃⋊C₈	—	3	2	no	—
158	C₂×C₃⋊C₈	—	9	2	no	—
159	ΓL(1,𝔽₂₅)	—	6	4	no	—
160	ΓL(1,𝔽₂₅)	—	18	4	no	—
161	C₂²×C₃²	—	2	1	no	—
162	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
163	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
164	C₂×C₃⋊D₃	—	2	1	no	—
165	C₂×C₃⋊D₃	—	2	1	no	—
166	C₂×C₃⋊D₃	C₃×C₄⋊C₄	1	2	yes	—
167	C₂×C₃×D₃	—	3	2	no	—
168	C₂×C₃×D₃	—	6	1	no	—
169	C₂×C₃×D₃	—	6	1	no	—
170	C₃²×C₄	—	2	1	no	—
171	C₃²×C₄	—	2	1	no	—
172	C₃²×C₄	—	2	2	no	—
173	C₃²×C₄	—	2	1	no	—
174	C₃²×C₄	—	2	1	no	—
175	C₃²×C₄	—	4	1	no	—
176	C₃²×C₄	ΓL(1,𝔽₂₅)	1	2	yes	complemented
177	C₃²×C₄	C₃×M₁₆	1	2	yes	complemented
178	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
179	C₃²×C₄	D₃×Q₈	1	1	yes	characteristic
180	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
181	C₃²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
182	C₃⋊Dic₃	—	2	1	no	—
183	C₃⋊Dic₃	C₃×C₄⋊C₄	1	2	yes	—
184	C₃⋊Dic₃	C₃×M₁₆	1	2	yes	complemented
185	C₃×Dic₃	—	3	2	no	—
186	C₃×Dic₃	—	3	2	no	—
187	C₃×Dic₃	—	6	1	no	—
188	C₂×M₁₆	—	9	2	no	—
189	C₂×C₄²	—	9	1	no	—
190	C₄⋊C₈	—	9	2	no	—
191	C₄⋊C₈	—	9	1	no	—
192	C₄⋊C₈	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
193	H(3,𝔽₃)	#423	1	1	yes	characteristic, complemented, Sylow
194	C₂³×C₃	—	9	1	no	—
195	C₂²×D₃	—	3	1	no	—
196	C₂²×D₃	—	9	1	no	—
197	C₂×C₃×C₄	—	3	1	no	—
198	C₂×C₃×C₄	—	3	1	no	—
199	C₂×C₃×C₄	—	3	1	no	—
200	C₂×C₃×C₄	—	3	1	no	—
201	C₂×C₃×C₄	—	3	1	no	—
202	C₂×C₃×C₄	—	3	1	no	—
203	C₂×C₃×C₄	—	6	1	no	—
204	C₂×C₃×C₄	—	6	1	no	—
205	C₂×C₃×C₄	—	6	1	no	—
206	C₂×C₃×C₄	—	9	2	no	—
207	C₂×C₃×C₄	—	9	2	no	—
208	C₂×C₃×C₄	—	9	1	no	—
209	C₂×C₃×C₄	—	9	1	no	—
210	C₂×C₃×C₄	—	9	1	no	—
211	C₂×C₃×C₄	—	18	2	no	—
212	C₂×C₃×C₄	—	18	2	no	—
213	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
214	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
216	C₂×Dic₃	—	3	1	no	—
217	C₂×Dic₃	—	3	1	no	—
218	C₂×Dic₃	—	3	1	no	—
219	C₂×Dic₃	—	9	1	no	—
220	C₂×Dic₃	—	9	1	no	—
221	C₂×Dic₃	—	9	1	no	—
222	C₄×D₃	—	3	2	no	—
223	C₄×D₃	—	3	2	no	—
224	C₄×D₃	—	6	2	no	—
225	C₄×D₃	—	6	2	no	—
226	C₄×D₃	—	9	2	no	—
227	C₄×D₃	—	9	2	no	—
228	C₄×D₃	—	18	2	no	—
229	C₄×D₃	—	18	2	no	—
230	C₃×C₈	—	2	2	no	—
231	C₃×C₈	—	6	2	no	—
232	C₃×C₈	—	6	2	no	—
233	C₃×C₈	—	12	2	no	—
234	C₃×C₈	—	18	2	no	—
235	C₃⋊C₈	—	6	2	no	—
236	C₃⋊C₈	—	18	2	no	—
237	C₂×C₃²	—	2	1	no	—
238	C₂×C₃²	—	2	1	no	—
239	C₂×C₃²	—	2	1	no	—
240	C₂×C₃²	D₃×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₃²	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
242	C₂×C₃²	D₃×M₁₆	1	1	yes	characteristic
243	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
245	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
246	C₃⋊D₃	—	2	2	no	—
247	C₃×D₃	—	6	2	no	—
248	C₂²×C₄	—	9	1	no	—
249	C₂²×C₄	—	9	1	no	—
250	C₂²×C₄	—	9	1	no	—
251	M₁₆	—	18	4	no	—
252	C₂×C₈	—	9	2	no	—
253	C₂×C₈	C₂×(C₃⋊D₃)⋊C₃	1	2	yes	—
254	C₄²	—	9	1	no	—
255	C₄²	—	9	1	no	—
256	C₄²	—	9	1	no	—
257	C₄²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
258	C₂²×C₃	—	3	1	no	—
259	C₂²×C₃	—	3	1	no	—
260	C₂²×C₃	—	6	1	no	—
261	C₂²×C₃	—	9	2	no	—
262	C₂²×C₃	—	18	1	no	—
263	C₂²×C₃	—	18	1	no	—
264	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
265	C₂×D₃	—	3	2	no	—
266	C₂×D₃	—	6	1	no	—
267	C₂×D₃	—	6	1	no	—
268	C₂×D₃	—	9	2	no	—
269	C₂×D₃	—	18	1	no	—
270	C₂×D₃	—	18	1	no	—
271	C₃×C₄	—	2	1	no	—
272	C₃×C₄	—	3	1	no	—
273	C₃×C₄	—	3	1	no	—
274	C₃×C₄	—	3	1	no	—
275	C₃×C₄	—	3	1	no	—
276	C₃×C₄	—	3	2	no	—
277	C₃×C₄	—	3	2	no	—
278	C₃×C₄	—	6	1	no	—
279	C₃×C₄	—	6	1	no	—
280	C₃×C₄	—	6	1	no	—
281	C₃×C₄	—	6	1	no	—
282	C₃×C₄	—	6	2	no	—
283	C₃×C₄	—	9	2	no	—
284	C₃×C₄	—	9	2	no	—
285	C₃×C₄	—	12	1	no	—
286	C₃×C₄	—	18	1	no	—
287	C₃×C₄	C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
288	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
289	C₃×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
290	Dic₃	—	3	2	no	—
291	Dic₃	—	3	2	no	—
292	Dic₃	—	6	1	no	—
293	Dic₃	—	9	2	no	—
294	Dic₃	—	9	2	no	—
295	Dic₃	—	18	1	no	—
296	C₃²	—	2	1	no	—
297	C₃²	#4837	1	1	yes	characteristic, complemented
298	C₃²	C₃×#423	1	1	yes	characteristic, complemented
299	C₂³	—	9	1	no	—
300	C₂×C₄	—	9	1	no	—
301	C₂×C₄	—	9	1	no	—
302	C₂×C₄	—	9	2	no	—
303	C₂×C₄	—	9	2	no	—
304	C₂×C₄	—	9	1	no	—
305	C₂×C₄	—	18	2	no	—
306	C₂×C₄	—	18	2	no	—
307	C₂×C₄	C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
308	C₂×C₄	C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
309	C₂×C₄	C₂²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	—	18	2	no	—
312	C₂×C₃	—	3	1	no	—
313	C₂×C₃	—	3	1	no	—
314	C₂×C₃	—	3	1	no	—
315	C₂×C₃	—	3	1	no	—
316	C₂×C₃	—	3	1	no	—
317	C₂×C₃	—	3	1	no	—
318	C₂×C₃	—	6	1	no	—
319	C₂×C₃	—	6	1	no	—
320	C₂×C₃	—	6	1	no	—
321	C₂×C₃	—	18	2	no	—
322	C₂×C₃	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₃	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
324	C₂×C₃	C₃×D₃×M₁₆	1	1	yes	characteristic
325	D₃	—	6	2	no	—
326	D₃	—	18	2	no	—
327	C₂²	—	9	2	no	—
328	C₂²	—	18	1	no	—
329	C₂²	—	18	1	no	—
330	C₂²	C₂×C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
331	C₄	—	2	1	no	—
332	C₄	—	9	2	no	—
333	C₄	—	9	2	no	—
334	C₄	—	18	1	no	—
335	C₄	#3743⋊C₃	1	2	yes	complemented
336	C₄	D₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
337	C₄	Q₈×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
338	C₃	—	3	1	no	—
339	C₃	—	3	1	no	—
340	C₃	—	6	1	no	—
341	C₃	C₃×#4837	1	1	yes	characteristic
342	C₂	—	18	2	no	—
343	C₂	C₄⋊C₄×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
344	C₂	C₂×#3743⋊C₃	1	1	yes	characteristic
345	C₂	M₁₆×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×(C₃⋊D₃)⋊C₃
commutator	C₂²×C₃²	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	H(3,𝔽₃)×C₄⋊C₈	C₂
socle	C₂²×C₃	C₂×C₃×C₄×D₃
prime radical	C₂²×(C₃⋊D₃)⋊C₃	C₂×C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₄⋊C₈	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₃×#423
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. H(3,𝔽₃)×C₄⋊C₈	C₂	semidirect
4. #63641⋊C₃	C₂	semidirect
5. C₄⋊((C₃⋊(C₃⋊C₈))⋊C₃)	C₂	semidirect
6. #10592536	C₃	semidirect
23. C₃²×C₄⋊C₈	D₃	semidirect
24. C₃²×C₄⋊C₈	C₂×C₃	semidirect
25. #63641	C₂×C₃	semidirect
26. C₄⋊(C₃⋊(C₃⋊C₈))	C₂×C₃	semidirect
72. C₄×H(3,𝔽₃)	M₁₆	semidirect
77. (C₃⋊Dic₃)⋊C₃	M₁₆	semidirect
176. C₃²×C₄	ΓL(1,𝔽₂₅)	semidirect
177. C₃²×C₄	C₃×M₁₆	semidirect
184. C₃⋊Dic₃	C₃×M₁₆	semidirect
192. C₄⋊C₈	(C₃⋊D₃)⋊C₃	semidirect
193. H(3,𝔽₃)	#423	semidirect
297. C₃²	#4837	semidirect
298. C₃²	C₃×#423	semidirect
335. C₄	#3743⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3743⋊C₃	2
C₄²×(C₃⋊D₃)⋊C₃	2
H(3,𝔽₃)×C₄⋊C₈	2
#63641⋊C₃	2
C₄⋊((C₃⋊(C₃⋊C₈))⋊C₃)	2
#10592536	3
C₃×#4837	3

Subgroups — #10592536⋊C3 #13142045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10592536⋊C₃ #13142045