Subgroups — C₃×#78561 #11860678

Order 1152.

1121 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	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#5521	C₂	1	2	yes	maximal, complemented
3	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5131	C₂	1	2	yes	maximal, complemented
5	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4711	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×D₂₄	C₂	1	4	yes	maximal, complemented
8	C₃×#2948	—	3	1	no	maximal
9	#78561	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
11	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₃²×#117	C₂²	1	1	yes	characteristic
14	C₃×#926	C₂²	1	2	yes	—
15	C₂×C₃×D₂₄	C₄	1	8	yes	complemented
16	C₂×C₃×D₂₄	C₂²	1	2	yes	—
17	C₂×C₃×D₂₄	C₂²	1	2	yes	—
18	C₃×#893	—	2	4	no	—
19	C₃×D₃×C₂²⋊C₄	—	2	4	no	—
20	C₃×C₄×D₁₂	C₂²	1	8	yes	complemented
21	C₃²×#97	C₂²	1	2	yes	complemented
22	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
23	C₃×#821	C₂²	1	8	yes	complemented
24	C₃×#818	C₂²	1	2	yes	complemented
25	C₃×#817	C₂²	1	2	yes	complemented
26	C₂²×C₃×D₈	—	3	1	no	—
27	C₃×#518	—	3	2	no	—
28	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
29	#5521	C₂×C₃	1	2	yes	complemented
30	C₃×#442	—	3	4	no	—
31	C₃×C₄×D₈	—	3	4	no	—
32	C₃×#427	—	3	1	no	—
33	C₃×#418	—	3	2	no	—
34	C₃×#405	—	2	1	no	—
35	C₃×#405	D₃	1	1	yes	characteristic, complemented
36	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
37	#5131	C₂×C₃	1	2	yes	complemented
38	#5106	C₂×C₃	1	1	yes	characteristic, complemented
39	#4711	C₂×C₃	1	4	yes	complemented
40	C₄×D₂₄	C₂×C₃	1	4	yes	complemented
41	C₂³×C₃×D₃	—	2	2	no	—
42	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
43	C₂×C₃×D₁₂	—	2	2	no	—
44	C₂×C₃×D₁₂	—	2	4	no	—
45	C₂×C₃×D₁₂	C₂×C₄	1	8	yes	complemented
46	C₂×C₃×D₁₂	C₂³	1	4	yes	—
47	C₂×C₃×C₄×D₃	—	2	8	no	—
48	C₃²×M₁₆	—	2	2	no	—
49	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃²×C₈	C₂³	1	2	yes	—
51	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
53	C₃²×C₄⋊C₄	D₄	1	2	yes	—
54	C₃²×C₂²⋊C₄	D₄	1	2	yes	—
55	C₃²×C₄²	C₂³	1	2	yes	—
56	C₃×#217	—	2	2	no	—
57	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
58	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
59	C₃×C₄×Dic₃	—	2	2	no	—
60	C₃×D₂₄	C₂×C₄	1	8	yes	complemented
61	C₃×D₂₄	C₂×C₄	1	8	yes	complemented
62	#2948	—	3	1	no	Sylow
63	C₂²×C₃×D₄	—	3	2	no	—
64	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
65	C₂×C₃×D₈	—	3	8	no	—
66	C₂×C₃×D₈	—	3	2	no	—
67	C₂×C₃×D₈	—	3	2	no	—
68	C₂×C₃×M₁₆	—	2	1	no	—
69	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×C₈	—	2	1	no	—
72	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₃×C₄×D₄	—	3	8	no	—
75	C₃×C₄×D₄	—	6	4	no	—
76	C₃×#117	—	2	1	no	—
77	C₃×#117	—	3	2	no	—
78	C₃×#117	C₂×D₃	1	1	yes	characteristic
79	C₃×#117	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
81	#926	C₂²×C₃	1	2	yes	—
82	C₂×D₂₄	C₃×C₄	1	8	yes	complemented
83	C₂×D₂₄	C₂²×C₃	1	2	yes	—
84	C₂×D₂₄	C₂²×C₃	1	2	yes	—
85	#893	—	2	4	no	—
86	D₃×C₂²⋊C₄	—	2	4	no	—
87	C₄×D₁₂	C₂²×C₃	1	8	yes	complemented
88	C₃×#107	—	3	2	no	—
89	C₃×#106	—	3	2	no	—
90	C₃×#102	—	3	8	no	—
91	C₃×#97	—	2	2	no	—
92	C₃×#97	C₂×D₃	1	2	yes	complemented
93	C₃×#97	C₂²×C₃	1	2	yes	complemented
94	C₃×C₄×C₈	—	2	2	no	—
95	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
96	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
97	#821	C₂²×C₃	1	8	yes	complemented
98	#818	C₂²×C₃	1	2	yes	complemented
99	#817	C₂²×C₃	1	2	yes	complemented
100	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×D₃	—	2	4	no	—
102	C₂²×C₃×D₃	—	2	8	no	—
103	C₂²×C₃×D₃	—	8	4	no	—
104	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
105	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	#41	1	2	yes	—
108	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×Dic₃	—	2	4	no	—
110	C₃×D₁₂	—	2	8	no	—
111	C₃×D₁₂	—	2	4	no	—
112	C₃×D₁₂	C₂²×C₄	1	8	yes	—
113	C₃×C₄×D₃	—	8	8	no	—
114	C₃²×C₈	—	2	2	no	—
115	C₃²×C₈	C₂²×C₄	1	2	yes	—
116	C₃²×C₈	C₂²×C₄	1	2	yes	—
117	C₂²×D₈	—	3	1	no	—
118	#518	—	3	2	no	—
119	#442	—	3	4	no	—
120	C₄×D₈	—	3	4	no	—
121	#427	—	3	1	no	—
122	#418	—	3	2	no	—
123	#405	C₃×D₃	1	1	yes	characteristic, complemented
124	C₂⁴×C₃	—	6	2	no	—
125	C₂³×D₃	—	2	2	no	—
126	C₂×C₃×D₄	—	3	8	no	—
127	C₂×C₃×D₄	—	3	4	no	—
128	C₂×C₃×D₄	—	6	2	no	—
129	C₂×C₃×D₄	—	6	4	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	6	8	no	—
132	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
134	C₂×D₁₂	—	2	2	no	—
135	C₂×D₁₂	—	2	4	no	—
136	C₂×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
137	C₂×D₁₂	C₂³×C₃	1	4	yes	—
138	C₂×C₄×D₃	—	2	8	no	—
139	C₃×D₈	—	3	8	no	—
140	C₃×D₈	—	3	8	no	—
141	C₃×M₁₆	—	2	4	no	—
142	C₃×M₁₆	—	2	2	no	—
143	C₃×M₁₆	—	2	2	no	—
144	C₂×C₃×C₈	—	2	4	no	—
145	C₂×C₃×C₈	—	2	1	no	—
146	C₂×C₃×C₈	—	2	2	no	—
147	C₂×C₃×C₈	—	2	1	no	—
148	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
149	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
150	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
151	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
153	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
154	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	2	2	no	—
157	C₃×C₄⋊C₄	—	3	4	no	—
158	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
159	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
160	C₃×C₂²⋊C₄	—	2	2	no	—
161	C₃×C₂²⋊C₄	—	6	2	no	—
162	C₃×C₂²⋊C₄	—	6	8	no	—
163	C₃×C₂²⋊C₄	D₁₂	1	2	yes	—
164	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
165	C₃×C₄²	—	2	2	no	—
166	C₃×C₄²	—	6	2	no	—
167	C₃×C₄²	C₂²×D₃	1	2	yes	—
168	C₃×C₄²	C₂³×C₃	1	2	yes	—
169	#217	—	2	2	no	—
170	(C₂×D₃)⋊C₄	—	2	8	no	—
171	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
172	C₄×Dic₃	—	2	2	no	—
173	D₂₄	C₂×C₃×C₄	1	8	yes	complemented
174	D₂₄	C₂×C₃×C₄	1	8	yes	complemented
175	C₂²×C₃²	—	2	2	no	—
176	C₂²×C₃²	C₄×D₄	1	2	yes	—
177	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₃×D₃	—	2	8	no	—
179	C₂×C₃×D₃	—	4	8	no	—
180	C₂×C₃×D₃	—	8	8	no	—
181	C₃²×C₄	—	2	4	no	—
182	C₃²×C₄	C₄×D₄	1	2	yes	—
183	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
184	C₃²×C₄	C₂×#41	1	1	yes	characteristic
185	C₃×Dic₃	—	4	4	no	—
186	C₂²×D₄	—	3	2	no	—
187	C₂×D₈	—	3	8	no	—
188	C₂×D₈	—	3	2	no	—
189	C₂×D₈	—	3	2	no	—
190	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
191	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
192	C₄×D₄	—	3	8	no	—
193	C₄×D₄	—	6	4	no	—
194	#117	—	3	2	no	—
195	#117	C₂×C₃×D₃	1	1	yes	characteristic
196	C₂×C₂²⋊C₄	—	6	4	no	—
197	#107	—	3	2	no	—
198	#106	—	3	2	no	—
199	#102	—	3	8	no	—
200	#97	C₂×C₃×D₃	1	2	yes	complemented
201	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
202	C₂³×C₃	—	2	1	no	—
203	C₂³×C₃	—	6	4	no	—
204	C₂³×C₃	—	6	8	no	—
205	C₂³×C₃	—	24	4	no	—
206	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
207	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂²×D₃	—	2	4	no	—
209	C₂²×D₃	—	2	8	no	—
210	C₂²×D₃	—	8	4	no	—
211	C₃×D₄	—	3	8	no	—
212	C₃×D₄	—	6	8	no	—
213	C₃×D₄	—	6	4	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	6	4	no	—
220	C₂×C₃×C₄	—	24	8	no	—
221	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
222	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
223	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
224	C₂×C₃×C₄	#235	1	2	yes	—
225	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
226	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
227	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₃×#41	1	2	yes	—
229	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
231	C₂×Dic₃	—	2	4	no	—
232	D₁₂	—	2	8	no	—
233	D₁₂	—	2	4	no	—
234	D₁₂	C₂²×C₃×C₄	1	8	yes	—
235	C₄×D₃	—	8	8	no	—
236	C₃×C₈	—	2	4	no	—
237	C₃×C₈	—	2	2	no	—
238	C₃×C₈	—	2	2	no	—
239	C₃×C₈	—	2	2	no	—
240	C₃×C₈	—	2	2	no	—
241	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
242	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
243	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
244	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
245	C₂×C₃²	—	2	2	no	—
246	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂×C₃²	#576	1	2	yes	—
248	C₃×D₃	—	4	8	no	—
249	C₂⁴	—	6	2	no	—
250	C₂×D₄	—	3	4	no	—
251	C₂×D₄	—	3	8	no	—
252	C₂×D₄	—	6	2	no	—
253	C₂×D₄	—	6	4	no	—
254	C₂²×C₄	—	6	8	no	—
255	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
256	D₈	—	3	8	no	—
257	D₈	—	3	8	no	—
258	M₁₆	—	2	2	no	—
259	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
260	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
261	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
262	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
263	C₄⋊C₄	—	3	4	no	—
264	C₄⋊C₄	C₃×D₁₂	1	2	yes	—
265	C₂²⋊C₄	—	6	2	no	—
266	C₂²⋊C₄	—	6	8	no	—
267	C₂²⋊C₄	C₃×D₁₂	1	2	yes	—
268	C₄²	—	6	2	no	—
269	C₄²	C₂²×C₃×D₃	1	2	yes	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	2	2	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	4	2	no	—
275	C₂²×C₃	—	6	8	no	—
276	C₂²×C₃	—	12	8	no	—
277	C₂²×C₃	—	24	8	no	—
278	C₂²×C₃	C₄×D₁₂	1	2	yes	—
279	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
280	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
281	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
282	C₂×D₃	—	2	8	no	—
283	C₂×D₃	—	4	8	no	—
284	C₂×D₃	—	8	8	no	—
285	C₃×C₄	—	2	4	no	—
286	C₃×C₄	—	2	4	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	4	4	no	—
291	C₃×C₄	—	12	4	no	—
292	C₃×C₄	C₄×D₁₂	1	2	yes	—
293	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
294	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
295	C₃×C₄	C₂×#235	1	1	yes	characteristic
296	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
297	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
298	Dic₃	—	4	4	no	—
299	C₃²	#2948	1	1	yes	characteristic, complemented, Sylow
300	C₂³	—	6	4	no	—
301	C₂³	—	6	8	no	—
302	C₂³	—	24	4	no	—
303	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
304	D₄	—	3	8	no	—
305	D₄	—	6	4	no	—
306	D₄	—	6	8	no	—
307	C₂×C₄	—	6	4	no	—
308	C₂×C₄	—	24	8	no	—
309	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
310	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
311	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
312	C₂×C₄	C₃×#235	1	2	yes	—
313	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
314	C₈	—	2	2	no	—
315	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
316	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
317	C₂×C₃	—	2	2	no	—
318	C₂×C₃	—	2	2	no	—
319	C₂×C₃	—	2	2	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	4	2	no	—
322	C₂×C₃	—	12	8	no	—
323	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
324	C₂×C₃	#5752	1	2	yes	—
325	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
326	C₂×C₃	C₃×#576	1	2	yes	—
327	D₃	—	4	8	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	6	8	no	—
330	C₂²	—	12	8	no	—
331	C₂²	—	24	8	no	—
332	C₂²	C₃×C₄×D₁₂	1	2	yes	—
333	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
334	C₄	—	2	4	no	—
335	C₄	—	12	4	no	—
336	C₄	C₃×C₄×D₁₂	1	2	yes	—
337	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
338	C₄	C₂×C₃×#235	1	1	yes	characteristic
339	C₃	—	2	1	no	—
340	C₃	#78561	1	1	yes	characteristic, direct product factor
341	C₃	C₃×#2948	1	1	yes	characteristic, complemented
342	C₂	—	2	2	no	—
343	C₂	—	12	8	no	—
344	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
345	C₂	C₃×#5752	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃×D₂₄	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2948
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
2. C₃×#5521	C₂	semidirect
3. C₃²×#405	C₂	semidirect
4. C₃×#5131	C₂	semidirect
5. C₃×#5106	C₂	semidirect
6. C₃×#4711	C₂	semidirect
7. C₃×C₄×D₂₄	C₂	semidirect
9. #78561	C₃	direct (N × H)
15. C₂×C₃×D₂₄	C₄	semidirect
20. C₃×C₄×D₁₂	C₂²	semidirect
21. C₃²×#97	C₂²	semidirect
22. C₃²×C₄×C₈	C₂²	semidirect
23. C₃×#821	C₂²	semidirect
24. C₃×#818	C₂²	semidirect
25. C₃×#817	C₂²	semidirect
29. #5521	C₂×C₃	semidirect
35. C₃×#405	D₃	semidirect
36. C₃×#405	C₂×C₃	semidirect
37. #5131	C₂×C₃	semidirect
38. #5106	C₂×C₃	semidirect
39. #4711	C₂×C₃	semidirect
40. C₄×D₂₄	C₂×C₃	semidirect
45. C₂×C₃×D₁₂	C₂×C₄	semidirect
49. C₂×C₃²×C₈	C₂×C₄	semidirect
60. C₃×D₂₄	C₂×C₄	semidirect
61. C₃×D₂₄	C₂×C₄	semidirect
82. C₂×D₂₄	C₃×C₄	semidirect
87. C₄×D₁₂	C₂²×C₃	semidirect
92. C₃×#97	C₂×D₃	semidirect
93. C₃×#97	C₂²×C₃	semidirect
95. C₃×C₄×C₈	C₂×D₃	semidirect
96. C₃×C₄×C₈	C₂²×C₃	semidirect
97. #821	C₂²×C₃	semidirect
98. #818	C₂²×C₃	semidirect
99. #817	C₂²×C₃	semidirect
123. #405	C₃×D₃	semidirect
136. C₂×D₁₂	C₂×C₃×C₄	semidirect
148. C₂×C₃×C₈	C₄×D₃	semidirect
149. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
173. D₂₄	C₂×C₃×C₄	semidirect
174. D₂₄	C₂×C₃×C₄	semidirect
200. #97	C₂×C₃×D₃	semidirect
201. C₄×C₈	C₂×C₃×D₃	semidirect
259. C₂×C₈	C₃×C₄×D₃	semidirect
299. C₃²	#2948	semidirect
340. C₃	#78561	direct (N × H)
341. C₃	C₃×#2948	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₂₄	2
C₃×#5521	2
C₃²×#405	2
C₃×#5131	2
C₃×#5106	2
C₃×#4711	2
C₃×C₄×D₂₄	2
C₃×#2948	3
#78561	3

Subgroups — C3×#78561 #11860678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78561 #11860678