Subgroups — #13179899

Order 1728.

3752 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11724684	C₂	1	1	yes	maximal, characteristic, complemented
2	#11724679	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	#11723991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88860	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723957	C₂	1	2	yes	maximal, complemented
7	#11723955	C₂	1	2	yes	maximal, complemented
8	#11723952	C₂	1	2	yes	maximal, complemented
9	D₈×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
10	#11723949	C₂	1	1	yes	maximal, characteristic, complemented
11	#11723948	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596245	—	3	13	no	maximal
13	C₃³×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×#6312	—	2	2	no	—
16	#89080	C₂²	1	2	yes	complemented
17	#89078	—	2	1	no	—
18	#89078	C₂²	1	2	yes	complemented
19	D₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
20	D₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
21	D₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
22	D₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
23	#89076	—	2	1	no	—
24	#89076	C₂²	1	1	yes	characteristic
25	#89076	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	—	2	1	no	—
27	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic, complemented
28	C₃³×SD₁₆	C₂²	1	2	yes	complemented
29	C₃³×D₈	C₂²	1	2	yes	complemented
30	C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	#88863	C₂²	1	1	yes	characteristic, complemented
32	#88862	C₂²	1	1	yes	characteristic, complemented
33	#88861	C₂²	1	1	yes	characteristic, complemented
34	#88860	C₂²	1	1	yes	characteristic, complemented
35	#88860	C₂²	1	2	yes	complemented
36	#88860	C₂²	1	2	yes	complemented
37	C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic, complemented
38	#88852	C₂²	1	2	yes	complemented
39	#88851	C₂²	1	2	yes	complemented
40	#88850	C₂²	1	2	yes	complemented
41	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
42	#64366	—	3	13	no	—
43	#64361	—	3	13	no	—
44	C₃²×AGL(1,ℤ/8)	D₃	1	13	yes	complemented
45	#64159	—	3	13	no	—
46	C₂×#3753	—	3	13	no	—
47	#64125	—	3	26	no	—
48	#64123	—	3	26	no	—
49	#64120	—	3	26	no	—
50	D₈×C₃⋊D₃	—	3	26	no	—
51	#64117	—	3	13	no	—
52	#64116	—	3	13	no	—
53	C₂³×C₃³	—	2	1	no	—
54	C₂²×C₃⋊(C₃⋊D₃)	—	2	1	no	—
55	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
56	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
57	C₃³×Q₈	C₂³	1	1	yes	characteristic
58	C₃³×D₄	—	2	1	no	—
59	C₃³×D₄	—	2	1	no	—
60	C₃³×D₄	C₂³	1	2	yes	—
61	C₃³×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₃³×C₄	—	2	1	no	—
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	#6312	—	2	1	no	—
65	#6312	—	2	2	no	—
66	#6312	—	2	2	no	—
67	#6312	—	2	2	no	—
68	#6312	D₄	1	2	yes	—
69	C₂×C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
70	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
71	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	1	no	—
72	C₄⋊(C₃⋊(C₃⋊D₃))	D₄	1	1	yes	characteristic
73	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	2	yes	—
74	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	1	yes	characteristic
75	C₄×C₃⋊(C₃⋊D₃)	—	2	1	no	—
76	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
77	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
78	#6308	D₄	1	1	yes	characteristic
79	#6308	C₂³	1	1	yes	characteristic
80	C₃³×C₈	C₂³	1	2	yes	—
81	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	1	yes	characteristic
82	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	1	yes	characteristic
83	#5774	—	9	13	no	—
84	C₃²×#41	C₂×D₃	1	13	yes	complemented
85	C₂×C₃²×D₄	C₂×D₃	1	13	yes	complemented
86	C₂×#638	—	6	26	no	—
87	#3832	—	3	26	no	—
88	#3830	—	3	26	no	—
89	#3830	—	6	13	no	—
90	D₄×C₃⋊D₃	—	3	26	no	—
91	D₄×C₃⋊D₃	—	3	26	no	—
92	D₄×C₃⋊D₃	—	6	13	no	—
93	D₄×C₃⋊D₃	—	6	26	no	—
94	#3828	—	3	13	no	—
95	#3828	—	3	13	no	—
96	#3828	—	6	13	no	—
97	C₂×C₄⋊(C₃⋊D₃)	—	3	13	no	—
98	C₂×C₄⋊(C₃⋊D₃)	—	6	13	no	—
99	C₃²×SD₁₆	C₂×D₃	1	26	yes	complemented
100	C₃²×D₈	C₂×D₃	1	26	yes	complemented
101	C₃²×M₁₆	C₂×D₃	1	13	yes	complemented
102	#3756	—	3	13	no	—
103	#3755	—	3	13	no	—
104	#3754	—	3	13	no	—
105	#3753	—	3	13	no	—
106	#3753	—	3	26	no	—
107	#3753	—	3	26	no	—
108	C₂×C₃⋊(C₃⋊C₈)	—	3	13	no	—
109	#3745	—	3	26	no	—
110	#3744	—	3	26	no	—
111	#3743	—	3	26	no	—
112	C₈×C₃⋊D₃	—	3	26	no	—
113	C₂²×C₃³	—	2	2	no	—
114	C₂²×C₃³	—	2	1	no	—
115	C₂²×C₃³	—	8	1	no	—
116	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
118	C₂×C₃⋊(C₃⋊D₃)	—	2	1	no	—
119	C₂×C₃⋊(C₃⋊D₃)	—	8	2	no	—
120	C₂×C₃⋊(C₃⋊D₃)	—	8	2	no	—
121	C₂×C₃⋊(C₃⋊D₃)	—	8	1	no	—
122	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	2	yes	—
123	C₃³×C₄	—	2	1	no	—
124	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
125	C₃³×C₄	C₂⁴	1	1	yes	characteristic
126	C₃⋊(C₃⋊Dic₃)	—	2	1	no	—
127	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	2	yes	—
128	#1009	—	9	13	no	—
129	#1004	—	9	13	no	—
130	C₃×AGL(1,ℤ/8)	C₃⋊D₃	1	13	yes	complemented
131	#950	—	9	13	no	—
132	C₂×#213	—	9	13	no	—
133	#916	—	9	26	no	—
134	#914	—	9	26	no	—
135	#911	—	9	26	no	—
136	D₃×D₈	—	9	26	no	—
137	#908	—	9	13	no	—
138	#907	—	9	13	no	—
139	C₂³×C₃²	—	2	13	no	—
140	C₂²×C₃⋊D₃	—	6	26	no	—
141	C₂²×C₃⋊D₃	—	6	26	no	—
142	C₂²×C₃⋊D₃	—	6	13	no	—
143	C₃²×Q₈	C₂²×D₃	1	13	yes	—
144	C₃²×D₄	—	2	13	no	—
145	C₃²×D₄	—	2	13	no	—
146	C₃²×D₄	C₂²×D₃	1	26	yes	—
147	C₃²×D₄	C₂²×D₃	1	13	yes	—
148	C₂×C₃²×C₄	—	2	13	no	—
149	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
150	#638	—	3	26	no	—
151	#638	—	6	26	no	—
152	#638	—	6	26	no	—
153	#638	—	6	26	no	—
154	#638	—	6	13	no	—
155	C₂×C₃⋊Dic₃	—	6	26	no	—
156	C₄⋊(C₃⋊D₃)	—	3	13	no	—
157	C₄⋊(C₃⋊D₃)	—	3	26	no	—
158	C₄⋊(C₃⋊D₃)	—	3	13	no	—
159	C₄⋊(C₃⋊D₃)	—	6	26	no	—
160	C₄⋊(C₃⋊D₃)	—	6	13	no	—
161	C₄×C₃⋊D₃	—	3	26	no	—
162	C₄×C₃⋊D₃	—	6	26	no	—
163	C₄×C₃⋊D₃	—	6	13	no	—
164	#634	—	3	13	no	—
165	#634	—	3	13	no	—
166	C₃²×C₈	C₂²×D₃	1	26	yes	—
167	C₃⋊(C₃⋊C₈)	—	3	13	no	—
168	C₃⋊(C₃⋊C₈)	—	3	13	no	—
169	#576	—	27	1	no	Sylow
170	C₂×C₃³	—	2	1	no	—
171	C₂×C₃³	—	4	1	no	—
172	C₂×C₃³	—	4	2	no	—
173	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
174	C₃⋊(C₃⋊D₃)	—	2	2	no	—
175	C₃⋊(C₃⋊D₃)	—	4	2	no	—
176	C₃⋊(C₃⋊D₃)	—	4	1	no	—
177	C₃×#41	C₂×C₃⋊D₃	1	13	yes	complemented
178	C₂×C₃×D₄	C₂×C₃⋊D₃	1	13	yes	complemented
179	C₂×#67	—	18	26	no	—
180	#239	—	9	26	no	—
181	#237	—	9	26	no	—
182	#237	—	18	13	no	—
183	D₃×D₄	—	9	26	no	—
184	D₃×D₄	—	9	26	no	—
185	D₃×D₄	—	18	13	no	—
186	D₃×D₄	—	18	26	no	—
187	#235	—	9	13	no	—
188	#235	—	9	13	no	—
189	#235	—	18	13	no	—
190	C₂×D₁₂	—	9	13	no	—
191	C₂×D₁₂	—	18	13	no	—
192	C₃×SD₁₆	C₂×C₃⋊D₃	1	26	yes	complemented
193	C₃×D₈	C₂×C₃⋊D₃	1	26	yes	complemented
194	C₃×M₁₆	C₂×C₃⋊D₃	1	13	yes	complemented
195	#216	—	9	13	no	—
196	#215	—	9	13	no	—
197	#214	—	9	13	no	—
198	#213	—	9	13	no	—
199	#213	—	9	26	no	—
200	#213	—	9	26	no	—
201	C₂×C₃⋊C₈	—	9	13	no	—
202	D₂₄	—	9	26	no	—
203	#204	—	9	26	no	—
204	ΓL(1,𝔽₂₅)	—	9	26	no	—
205	D₃×C₈	—	9	26	no	—
206	C₂²×C₃²	—	2	26	no	—
207	C₂²×C₃²	—	2	13	no	—
208	C₂²×C₃²	—	8	13	no	—
209	C₂²×C₃²	D₃×D₄	1	13	yes	—
210	C₂×C₃⋊D₃	—	3	26	no	—
211	C₂×C₃⋊D₃	—	6	26	no	—
212	C₂×C₃⋊D₃	—	6	13	no	—
213	C₂×C₃⋊D₃	—	24	26	no	—
214	C₂×C₃⋊D₃	—	24	26	no	—
215	C₂×C₃⋊D₃	—	24	13	no	—
216	C₃²×C₄	—	2	13	no	—
217	C₃²×C₄	D₃×D₄	1	13	yes	—
218	C₃²×C₄	C₂³×D₃	1	13	yes	—
219	C₃⋊Dic₃	—	3	26	no	—
220	C₃⋊Dic₃	—	6	13	no	—
221	H(5,𝔽₂)	—	27	1	no	—
222	H(5,𝔽₂)	—	27	1	no	—
223	AGL(1,ℤ/8)	—	27	2	no	—
224	AGL(1,ℤ/8)	—	27	2	no	—
225	AGL(1,ℤ/8)	—	27	1	no	—
226	AGL(1,ℤ/8)	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
227	#135	—	27	1	no	—
228	#135	—	27	2	no	—
229	C₂×D₈	—	27	1	no	—
230	C₂×D₈	—	27	2	no	—
231	#131	—	27	1	no	—
232	C₃³	#576	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₃	—	2	13	no	—
234	C₂²×D₃	—	18	26	no	—
235	C₂²×D₃	—	18	26	no	—
236	C₂²×D₃	—	18	13	no	—
237	C₃×Q₈	C₂²×C₃⋊D₃	1	13	yes	—
238	C₃×D₄	—	2	13	no	—
239	C₃×D₄	—	2	13	no	—
240	C₃×D₄	C₂²×C₃⋊D₃	1	26	yes	—
241	C₃×D₄	C₂²×C₃⋊D₃	1	13	yes	—
242	C₂×C₃×C₄	—	2	13	no	—
243	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
244	#67	—	9	26	no	—
245	#67	—	18	26	no	—
246	#67	—	18	26	no	—
247	#67	—	18	26	no	—
248	#67	—	18	13	no	—
249	C₂×Dic₃	—	18	26	no	—
250	D₁₂	—	9	26	no	—
251	D₁₂	—	9	13	no	—
252	D₁₂	—	9	13	no	—
253	D₁₂	—	18	26	no	—
254	D₁₂	—	18	13	no	—
255	C₄×D₃	—	9	26	no	—
256	C₄×D₃	—	18	26	no	—
257	C₄×D₃	—	18	13	no	—
258	Dic₆	—	9	13	no	—
259	Dic₆	—	9	13	no	—
260	C₃×C₈	C₂²×C₃⋊D₃	1	26	yes	—
261	C₃⋊C₈	—	9	13	no	—
262	C₃⋊C₈	—	9	13	no	—
263	C₂×C₃²	—	2	13	no	—
264	C₂×C₃²	—	4	13	no	—
265	C₂×C₃²	—	4	26	no	—
266	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
267	C₃⋊D₃	—	6	26	no	—
268	C₃⋊D₃	—	12	26	no	—
269	C₃⋊D₃	—	12	13	no	—
270	#41	—	27	1	no	—
271	#41	—	27	2	no	—
272	#41	—	27	2	no	—
273	#41	—	27	1	no	—
274	#41	—	54	1	no	—
275	#41	—	54	1	no	—
276	#41	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
277	C₂×D₄	—	27	2	no	—
278	C₂×D₄	—	27	2	no	—
279	C₂×D₄	—	27	1	no	—
280	C₂×D₄	—	54	1	no	—
281	C₂×D₄	—	54	2	no	—
282	C₂×D₄	—	54	1	no	—
283	C₂×D₄	—	54	2	no	—
284	C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
285	Q₁₆	—	27	1	no	—
286	SD₁₆	—	27	1	no	—
287	SD₁₆	—	27	1	no	—
288	SD₁₆	—	27	2	no	—
289	SD₁₆	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
290	D₈	—	27	2	no	—
291	D₈	—	27	1	no	—
292	D₈	—	27	2	no	—
293	D₈	—	27	2	no	—
294	D₈	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
295	M₁₆	—	27	2	no	—
296	M₁₆	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
297	C₂×C₈	—	27	1	no	—
298	C₂×C₈	—	27	2	no	—
299	C₂²×C₃	—	2	26	no	—
300	C₂²×C₃	—	2	13	no	—
301	C₂²×C₃	—	8	13	no	—
302	C₂²×C₃	D₄×C₃⋊D₃	1	13	yes	—
303	C₂×D₃	—	9	26	no	—
304	C₂×D₃	—	18	26	no	—
305	C₂×D₃	—	18	13	no	—
306	C₂×D₃	—	72	26	no	—
307	C₂×D₃	—	72	26	no	—
308	C₂×D₃	—	72	13	no	—
309	C₃×C₄	—	2	13	no	—
310	C₃×C₄	D₄×C₃⋊D₃	1	13	yes	—
311	C₃×C₄	C₂³×C₃⋊D₃	1	13	yes	—
312	Dic₃	—	9	26	no	—
313	Dic₃	—	18	13	no	—
314	C₃²	#5774	1	13	yes	complemented
315	C₂³	—	2	1	no	—
316	C₂³	—	54	2	no	—
317	C₂³	—	54	2	no	—
318	C₂³	—	54	1	no	—
319	Q₈	—	27	1	no	—
320	Q₈	—	27	1	no	—
321	Q₈	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
322	D₄	—	2	1	no	—
323	D₄	—	2	1	no	—
324	D₄	—	27	2	no	—
325	D₄	—	27	2	no	—
326	D₄	—	27	1	no	—
327	D₄	—	27	1	no	—
328	D₄	—	54	2	no	—
329	D₄	—	54	2	no	—
330	D₄	—	54	2	no	—
331	D₄	—	54	2	no	—
332	D₄	—	54	1	no	—
333	D₄	—	54	1	no	—
334	D₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
335	D₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	27	2	no	—
338	C₂×C₄	—	54	2	no	—
339	C₂×C₄	—	54	2	no	—
340	C₂×C₄	—	54	1	no	—
341	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
342	C₈	—	27	1	no	—
343	C₈	—	27	1	no	—
344	C₈	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
345	C₂×C₃	—	2	13	no	—
346	C₂×C₃	—	4	13	no	—
347	C₂×C₃	—	4	26	no	—
348	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
349	D₃	—	18	26	no	—
350	D₃	—	36	26	no	—
351	D₃	—	36	13	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	27	2	no	—
356	C₂²	—	54	2	no	—
357	C₂²	—	54	1	no	—
358	C₂²	—	216	1	no	—
359	C₂²	—	216	2	no	—
360	C₂²	—	216	2	no	—
361	C₂²	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	27	2	no	—
364	C₄	—	54	1	no	—
365	C₄	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
366	C₄	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
367	C₃	#10596245	1	13	yes	complemented
368	C₂	—	2	1	no	—
369	C₂	—	4	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	54	2	no	—
372	C₂	—	108	2	no	—
373	C₂	—	108	1	no	—
374	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)
commutator, cosocle	C₃³×C₄	C₂⁴
Frattini	C₄	C₂³×C₃⋊(C₃⋊D₃)
Fitting	C₃³×AGL(1,ℤ/8)	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	AGL(1,ℤ/8)	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	#576
LCS	G ▷ C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #11724684	C₂	semidirect
2. #11724679	C₂	semidirect
3. C₃³×AGL(1,ℤ/8)	C₂	semidirect
4. #11723991	C₂	semidirect
5. C₂×#88860	C₂	semidirect
6. #11723957	C₂	semidirect
7. #11723955	C₂	semidirect
8. #11723952	C₂	semidirect
9. D₈×C₃⋊(C₃⋊D₃)	C₂	semidirect
10. #11723949	C₂	semidirect
11. #11723948	C₂	semidirect
13. C₃³×#41	C₂²	semidirect
14. C₂×C₃³×D₄	C₂²	semidirect
16. #89080	C₂²	semidirect
18. #89078	C₂²	semidirect
21. D₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
22. D₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
25. #89076	C₂²	semidirect
27. C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	semidirect
28. C₃³×SD₁₆	C₂²	semidirect
29. C₃³×D₈	C₂²	semidirect
30. C₃³×M₁₆	C₂²	semidirect
31. #88863	C₂²	semidirect
32. #88862	C₂²	semidirect
33. #88861	C₂²	semidirect
34. #88860	C₂²	semidirect
35. #88860	C₂²	semidirect
36. #88860	C₂²	semidirect
37. C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
38. #88852	C₂²	semidirect
39. #88851	C₂²	semidirect
40. #88850	C₂²	semidirect
41. C₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
44. C₃²×AGL(1,ℤ/8)	D₃	semidirect
84. C₃²×#41	C₂×D₃	semidirect
85. C₂×C₃²×D₄	C₂×D₃	semidirect
99. C₃²×SD₁₆	C₂×D₃	semidirect
100. C₃²×D₈	C₂×D₃	semidirect
101. C₃²×M₁₆	C₂×D₃	semidirect
130. C₃×AGL(1,ℤ/8)	C₃⋊D₃	semidirect
177. C₃×#41	C₂×C₃⋊D₃	semidirect
178. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
192. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
193. C₃×D₈	C₂×C₃⋊D₃	semidirect
194. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
226. AGL(1,ℤ/8)	C₃⋊(C₃⋊D₃)	semidirect
232. C₃³	#576	semidirect
276. #41	C₂×C₃⋊(C₃⋊D₃)	semidirect
284. C₂×D₄	C₂×C₃⋊(C₃⋊D₃)	semidirect
289. SD₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
294. D₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
296. M₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
314. C₃²	#5774	semidirect
367. C₃	#10596245	semidirect

Maximal subgroups

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

subgroup	index
#11724684	2
#11724679	2
C₃³×AGL(1,ℤ/8)	2
#11723991	2
C₂×#88860	2
#11723957	2
#11723955	2
#11723952	2
D₈×C₃⋊(C₃⋊D₃)	2
#11723949	2
#11723948	2
#10596245	3