Subgroups — C₂×C₃×#4869 #11860147

Order 1152.

1281 conjugacy classes of subgroups.

The subgroup lattice has 337 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	C₂×C₃×#893	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#809	C₂	1	2	yes	maximal, complemented
6	C₃×#4869	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#442	—	3	1	no	maximal
8	C₂×#4869	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×D₃	—	2	2	no	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₂₄	C₄	1	8	yes	complemented
17	C₂×C₃×D₂₄	C₂²	1	4	yes	—
18	C₃×#893	—	2	4	no	—
19	C₃×#893	C₂²	1	8	yes	complemented
20	C₃²×#106	C₂²	1	4	yes	complemented
21	C₃×#815	C₂²	1	4	yes	complemented
22	C₃×#809	C₂²	1	8	yes	complemented
23	C₂²×C₃×D₈	—	3	1	no	—
24	C₂×C₃×C₄×D₄	—	3	2	no	—
25	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
26	C₂×#893	C₂×C₃	1	2	yes	complemented
27	C₃×#442	—	3	8	no	—
28	C₂×C₃×#106	—	2	1	no	—
29	C₂×C₃×#106	D₃	1	1	yes	characteristic, complemented
30	C₂×C₃×#106	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₃×#102	—	3	2	no	—
32	C₂×C₃×#97	—	3	1	no	—
33	C₂×#815	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#809	C₂×C₃	1	2	yes	complemented
35	#4869	C₂×C₃	1	8	yes	direct product factor
36	C₂³×C₃×D₃	—	2	2	no	—
37	C₂²×C₃²×C₄	—	2	2	no	—
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	D₄	1	2	yes	—
40	C₂×C₃×D₁₂	—	2	2	no	—
41	C₂×C₃×D₁₂	—	2	4	no	—
42	C₂×C₃×D₁₂	C₂×C₄	1	8	yes	complemented
43	C₂×C₃×D₁₂	C₂³	1	4	yes	—
44	C₂×C₃×C₄×D₃	—	2	8	no	—
45	C₂×C₃×C₄×D₃	—	4	8	no	—
46	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
47	C₂×C₃²×C₈	C₂³	1	2	yes	—
48	C₃²×C₄⋊C₄	—	2	2	no	—
49	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
50	C₃×(C₂×D₃)⋊C₄	—	2	8	no	—
51	C₃×C₄×Dic₃	D₄	1	2	yes	—
52	C₃×C₄×Dic₃	C₂³	1	2	yes	—
53	C₂×C₃×C₃⋊C₈	—	2	2	no	—
54	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
55	C₃×D₂₄	C₂×C₄	1	16	yes	complemented
56	C₂×#442	—	3	1	no	Sylow
57	C₂²×C₃×D₄	—	3	2	no	—
58	C₂³×C₃×C₄	—	6	2	no	—
59	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
60	C₂²×C₄×D₃	—	2	2	no	—
61	C₂×C₃×D₈	—	3	8	no	—
62	C₂×C₃×D₈	—	3	4	no	—
63	C₂²×C₃×C₈	—	2	1	no	—
64	C₂²×C₃×C₈	—	3	1	no	—
65	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
67	C₃×C₄×D₄	—	3	8	no	—
68	C₃×C₄×D₄	—	6	4	no	—
69	C₂×C₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
71	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
73	C₂×C₃×C₄²	—	3	1	no	—
74	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
75	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
77	C₂×D₂₄	C₃×C₄	1	8	yes	complemented
78	C₂×D₂₄	C₂²×C₃	1	4	yes	—
79	#893	—	2	4	no	—
80	#893	C₂²×C₃	1	8	yes	complemented
81	C₃×#106	—	2	4	no	—
82	C₃×#106	C₂×D₃	1	4	yes	complemented
83	C₃×#106	C₂²×C₃	1	4	yes	complemented
84	C₃×#102	—	3	8	no	—
85	C₃×#97	—	3	4	no	—
86	#815	C₂²×C₃	1	4	yes	complemented
87	#809	C₂²×C₃	1	8	yes	complemented
88	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₃×D₃	—	2	8	no	—
90	C₂²×C₃×D₃	—	2	4	no	—
91	C₂²×C₃×D₃	—	4	4	no	—
92	C₂²×C₃×D₃	—	4	4	no	—
93	C₂×C₃²×C₄	—	2	4	no	—
94	C₂×C₃²×C₄	—	4	4	no	—
95	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
96	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	#41	1	2	yes	—
98	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
99	C₂×C₃×Dic₃	—	2	4	no	—
100	C₂×C₃×Dic₃	C₂×D₄	1	4	yes	—
101	C₃×D₁₂	—	2	8	no	—
102	C₃×D₁₂	—	2	4	no	—
103	C₃×D₁₂	C₂²×C₄	1	8	yes	complemented
104	C₃×C₄×D₃	—	4	16	no	—
105	C₃²×C₈	C₂²×C₄	1	4	yes	complemented
106	C₃×C₃⋊C₈	—	2	2	no	—
107	C₂²×D₈	—	3	1	no	—
108	C₂×C₄×D₄	—	3	2	no	—
109	#442	—	3	8	no	—
110	C₂×#106	C₃×D₃	1	1	yes	characteristic, complemented
111	C₂×#102	—	3	2	no	—
112	C₂×#97	—	3	1	no	—
113	C₂⁴×C₃	—	6	2	no	—
114	C₂³×D₃	—	2	2	no	—
115	C₂×C₃×D₄	—	3	8	no	—
116	C₂×C₃×D₄	—	3	4	no	—
117	C₂×C₃×D₄	—	6	2	no	—
118	C₂×C₃×D₄	—	6	4	no	—
119	C₂²×C₃×C₄	—	2	2	no	—
120	C₂²×C₃×C₄	—	2	2	no	—
121	C₂²×C₃×C₄	—	2	1	no	—
122	C₂²×C₃×C₄	—	3	2	no	—
123	C₂²×C₃×C₄	—	4	2	no	—
124	C₂²×C₃×C₄	—	6	8	no	—
125	C₂²×C₃×C₄	—	12	8	no	—
126	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
127	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂²×Dic₃	C₃×D₄	1	2	yes	—
129	C₂×D₁₂	—	2	2	no	—
130	C₂×D₁₂	—	2	4	no	—
131	C₂×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
132	C₂×D₁₂	C₂³×C₃	1	4	yes	—
133	C₂×C₄×D₃	—	2	8	no	—
134	C₂×C₄×D₃	—	4	8	no	—
135	C₃×D₈	—	3	16	no	—
136	C₂×C₃×C₈	—	2	4	no	—
137	C₂×C₃×C₈	—	2	2	no	—
138	C₂×C₃×C₈	—	3	2	no	—
139	C₂×C₃×C₈	—	6	2	no	—
140	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
141	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
142	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
143	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
144	C₃×C₄⋊C₄	—	2	2	no	—
145	C₃×C₄⋊C₄	—	2	2	no	—
146	C₃×C₄⋊C₄	—	2	4	no	—
147	C₃×C₄⋊C₄	—	4	2	no	—
148	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
149	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
150	C₃×C₂²⋊C₄	—	6	8	no	—
151	C₃×C₄²	—	3	2	no	—
152	C₃×C₄²	—	3	2	no	—
153	(C₂×D₃)⋊C₄	—	2	8	no	—
154	C₄×Dic₃	C₃×D₄	1	2	yes	—
155	C₄×Dic₃	C₂³×C₃	1	2	yes	—
156	C₂×C₃⋊C₈	—	2	2	no	—
157	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
158	D₂₄	C₂×C₃×C₄	1	16	yes	complemented
159	C₂²×C₃²	C₄×D₄	1	2	yes	—
160	C₂²×C₃²	AGL(1,ℤ/8)	1	4	yes	—
161	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃×D₃	—	2	8	no	—
163	C₂×C₃×D₃	—	4	4	no	—
164	C₂×C₃×D₃	—	4	4	no	—
165	C₂×C₃×D₃	—	4	16	no	—
166	C₃²×C₄	—	4	4	no	—
167	C₃²×C₄	C₄×D₄	1	2	yes	—
168	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
169	C₃²×C₄	C₂×#41	1	1	yes	characteristic
170	C₃×Dic₃	—	2	4	no	—
171	C₂²×D₄	—	3	2	no	—
172	C₂³×C₄	—	6	2	no	—
173	C₂×D₈	—	3	8	no	—
174	C₂×D₈	—	3	4	no	—
175	C₂²×C₈	—	3	1	no	—
176	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
177	C₄×D₄	—	3	8	no	—
178	C₄×D₄	—	6	4	no	—
179	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
180	C₂×C₂²⋊C₄	—	6	2	no	—
181	C₂×C₄²	—	3	1	no	—
182	#106	C₂×C₃×D₃	1	4	yes	complemented
183	#102	—	3	8	no	—
184	#97	—	3	4	no	—
185	C₂³×C₃	—	2	1	no	—
186	C₂³×C₃	—	6	8	no	—
187	C₂³×C₃	—	6	4	no	—
188	C₂³×C₃	—	12	4	no	—
189	C₂³×C₃	—	12	4	no	—
190	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
191	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂²×D₃	—	2	8	no	—
193	C₂²×D₃	—	2	4	no	—
194	C₂²×D₃	—	4	4	no	—
195	C₂²×D₃	—	4	4	no	—
196	C₃×D₄	—	3	8	no	—
197	C₃×D₄	—	6	8	no	—
198	C₃×D₄	—	6	4	no	—
199	C₂×C₃×C₄	—	2	4	no	—
200	C₂×C₃×C₄	—	2	4	no	—
201	C₂×C₃×C₄	—	2	1	no	—
202	C₂×C₃×C₄	—	2	2	no	—
203	C₂×C₃×C₄	—	2	1	no	—
204	C₂×C₃×C₄	—	2	2	no	—
205	C₂×C₃×C₄	—	3	4	no	—
206	C₂×C₃×C₄	—	4	4	no	—
207	C₂×C₃×C₄	—	4	4	no	—
208	C₂×C₃×C₄	—	4	4	no	—
209	C₂×C₃×C₄	—	6	4	no	—
210	C₂×C₃×C₄	—	8	4	no	—
211	C₂×C₃×C₄	—	12	16	no	—
212	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
213	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
214	C₂×C₃×C₄	#239	1	2	yes	—
215	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
216	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄	C₃×#41	1	2	yes	—
218	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
220	C₂×Dic₃	—	2	4	no	—
221	C₂×Dic₃	C₂×C₃×D₄	1	4	yes	—
222	D₁₂	—	2	8	no	—
223	D₁₂	—	2	4	no	—
224	D₁₂	C₂²×C₃×C₄	1	8	yes	complemented
225	C₄×D₃	—	4	16	no	—
226	C₃×C₈	—	2	4	no	—
227	C₃×C₈	—	6	2	no	—
228	C₃×C₈	C₂×C₄×D₃	1	4	yes	complemented
229	C₃×C₈	C₂²×C₃×C₄	1	4	yes	complemented
230	C₃⋊C₈	—	2	2	no	—
231	C₂×C₃²	#442	1	4	yes	complemented
232	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	2	yes	—
234	C₃×D₃	—	4	8	no	—
235	C₂⁴	—	6	2	no	—
236	C₂×D₄	—	3	4	no	—
237	C₂×D₄	—	3	8	no	—
238	C₂×D₄	—	6	2	no	—
239	C₂×D₄	—	6	4	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	3	2	no	—
242	C₂²×C₄	—	6	8	no	—
243	C₂²×C₄	—	12	8	no	—
244	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
245	D₈	—	3	16	no	—
246	C₂×C₈	—	3	2	no	—
247	C₂×C₈	—	6	2	no	—
248	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
249	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
252	C₂²⋊C₄	—	6	8	no	—
253	C₄²	—	3	2	no	—
254	C₄²	—	3	2	no	—
255	C₂²×C₃	—	2	2	no	—
256	C₂²×C₃	—	2	4	no	—
257	C₂²×C₃	—	2	1	no	—
258	C₂²×C₃	—	6	8	no	—
259	C₂²×C₃	—	12	16	no	—
260	C₂²×C₃	—	12	4	no	—
261	C₂²×C₃	—	12	4	no	—
262	C₂²×C₃	#893	1	2	yes	—
263	C₂²×C₃	#914	1	4	yes	—
264	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
265	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	4	yes	—
266	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
267	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
268	C₂×D₃	—	2	8	no	—
269	C₂×D₃	—	4	4	no	—
270	C₂×D₃	—	4	4	no	—
271	C₂×D₃	—	4	16	no	—
272	C₃×C₄	—	2	2	no	—
273	C₃×C₄	—	2	1	no	—
274	C₃×C₄	—	2	1	no	—
275	C₃×C₄	—	4	4	no	—
276	C₃×C₄	—	4	4	no	—
277	C₃×C₄	—	6	4	no	—
278	C₃×C₄	—	8	4	no	—
279	C₃×C₄	#893	1	2	yes	—
280	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
281	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
282	C₃×C₄	C₂×#239	1	1	yes	characteristic
283	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
284	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
285	Dic₃	—	2	4	no	—
286	C₃²	C₂×#442	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	6	8	no	—
288	C₂³	—	6	4	no	—
289	C₂³	—	12	4	no	—
290	C₂³	—	12	4	no	—
291	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
292	D₄	—	3	8	no	—
293	D₄	—	6	8	no	—
294	D₄	—	6	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	3	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	6	4	no	—
299	C₂×C₄	—	12	16	no	—
300	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
301	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
302	C₂×C₄	C₃×#239	1	2	yes	—
303	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
304	C₈	—	6	2	no	—
305	C₈	C₂×C₃×C₄×D₃	1	4	yes	complemented
306	C₂×C₃	—	2	1	no	—
307	C₂×C₃	—	2	2	no	—
308	C₂×C₃	—	2	4	no	—
309	C₂×C₃	—	12	8	no	—
310	C₂×C₃	#4869	1	4	yes	direct product factor
311	C₂×C₃	C₃×#442	1	4	yes	complemented
312	C₂×C₃	C₂×#893	1	1	yes	characteristic
313	C₂×C₃	C₂×#914	1	2	yes	—
314	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
315	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
316	D₃	—	4	8	no	—
317	C₂²	—	6	8	no	—
318	C₂²	—	12	4	no	—
319	C₂²	—	12	4	no	—
320	C₂²	—	12	16	no	—
321	C₂²	C₃×#893	1	2	yes	—
322	C₂²	C₃×#914	1	4	yes	—
323	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
324	C₄	—	4	4	no	—
325	C₄	—	6	4	no	—
326	C₄	C₃×#893	1	2	yes	—
327	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
328	C₄	C₂×C₃×#239	1	1	yes	characteristic
329	C₃	—	2	1	no	—
330	C₃	C₂×#4869	1	1	yes	characteristic, direct product factor
331	C₃	C₂×C₃×#442	1	1	yes	characteristic, complemented
332	C₂	—	12	8	no	—
333	C₂	C₃×#4869	1	4	yes	direct product factor
334	C₂	C₂×C₃×#893	1	1	yes	characteristic
335	C₂	C₂×C₃×#914	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#106	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₂₄	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#106	D₃
hypocenter	C₃	C₂×C₃×#442
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#106

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#893	C₂	semidirect
3. C₂×C₃²×#106	C₂	semidirect
4. C₂×C₃×#815	C₂	semidirect
5. C₂×C₃×#809	C₂	semidirect
6. C₃×#4869	C₂	direct (N × H)
8. C₂×#4869	C₃	direct (N × H)
16. C₂×C₃×D₂₄	C₄	semidirect
19. C₃×#893	C₂²	semidirect
20. C₃²×#106	C₂²	semidirect
21. C₃×#815	C₂²	semidirect
22. C₃×#809	C₂²	semidirect
26. C₂×#893	C₂×C₃	semidirect
29. C₂×C₃×#106	D₃	semidirect
30. C₂×C₃×#106	C₂×C₃	semidirect
33. C₂×#815	C₂×C₃	semidirect
34. C₂×#809	C₂×C₃	semidirect
35. #4869	C₂×C₃	direct (N × H)
42. C₂×C₃×D₁₂	C₂×C₄	semidirect
46. C₂×C₃²×C₈	C₂×C₄	semidirect
55. C₃×D₂₄	C₂×C₄	semidirect
77. C₂×D₂₄	C₃×C₄	semidirect
80. #893	C₂²×C₃	semidirect
82. C₃×#106	C₂×D₃	semidirect
83. C₃×#106	C₂²×C₃	semidirect
86. #815	C₂²×C₃	semidirect
87. #809	C₂²×C₃	semidirect
103. C₃×D₁₂	C₂²×C₄	semidirect
105. C₃²×C₈	C₂²×C₄	semidirect
110. C₂×#106	C₃×D₃	semidirect
131. C₂×D₁₂	C₂×C₃×C₄	semidirect
140. C₂×C₃×C₈	C₄×D₃	semidirect
141. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
158. D₂₄	C₂×C₃×C₄	semidirect
182. #106	C₂×C₃×D₃	semidirect
224. D₁₂	C₂²×C₃×C₄	semidirect
228. C₃×C₈	C₂×C₄×D₃	semidirect
229. C₃×C₈	C₂²×C₃×C₄	semidirect
231. C₂×C₃²	#442	semidirect
248. C₂×C₈	C₃×C₄×D₃	semidirect
286. C₃²	C₂×#442	semidirect
305. C₈	C₂×C₃×C₄×D₃	semidirect
310. C₂×C₃	#4869	direct (N × H)
311. C₂×C₃	C₃×#442	semidirect
330. C₃	C₂×#4869	direct (N × H)
331. C₃	C₂×C₃×#442	semidirect
333. C₂	C₃×#4869	direct (N × H)

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
C₂×C₃×#893	2
C₂×C₃²×#106	2
C₂×C₃×#815	2
C₂×C₃×#809	2
C₃×#4869	2
C₂×C₃×#442	3
C₂×#4869	3

Subgroups — C2×C3×#4869 #11860147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4869 #11860147