Subgroups — C₂×C₃×#64367 #13181742

Order 1728.

5420 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64367	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×Q₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#3830	C₂	1	6	yes	maximal, complemented
5	C₂×C₃×#3828	C₂	1	3	yes	maximal, complemented
6	C₂²×C₃×#634	C₂	1	3	yes	maximal, complemented
7	C₂×#64367	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#1010	—	3	4	no	maximal
9	C₃³×#41	C₂²	1	8	yes	complemented
10	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃³×D₄	C₂²	1	3	yes	—
12	C₂²×C₃³×C₄	C₂²	1	3	yes	—
13	C₂×C₃×#638	C₂²	1	6	yes	—
14	C₂²×C₃×C₃⋊Dic₃	C₂²	1	6	yes	—
15	C₃×Q₈×C₃⋊D₃	C₂²	1	16	yes	complemented
16	C₃×#3830	C₂²	1	48	yes	complemented
17	C₃×#3828	C₂²	1	24	yes	complemented
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	6	yes	—
20	C₂×C₃×#634	C₂²	1	3	yes	—
21	C₂×C₃×#634	C₂²	1	6	yes	—
22	C₂×C₃×#634	C₂²	1	24	yes	complemented
23	C₂×C₃²×#41	—	2	4	no	—
24	C₂×C₃²×#41	D₃	1	4	yes	complemented
25	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic, complemented
26	#64367	C₂×C₃	1	16	yes	direct product factor
27	C₂×Q₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
28	C₂×#3830	C₂×C₃	1	6	yes	complemented
29	C₂×#3828	C₂×C₃	1	3	yes	complemented
30	C₂²×#634	C₂×C₃	1	3	yes	complemented
31	C₃×#1010	—	3	64	no	—
32	C₂×C₃×D₃×Q₈	—	3	8	no	—
33	C₂×C₃×#237	—	3	24	no	—
34	C₂×C₃×#235	—	3	12	no	—
35	C₂²×C₃×Dic₆	—	3	12	no	—
36	C₂³×C₃³	C₂³	1	3	yes	—
37	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
38	C₃³×Q₈	C₂³	1	4	yes	—
39	C₃³×D₄	C₂³	1	12	yes	—
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃³×C₄	C₂³	1	3	yes	—
42	C₂×C₃³×C₄	C₂³	1	12	yes	—
43	C₃×#638	C₂³	1	24	yes	—
44	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	—
45	C₂×C₃×C₃⋊Dic₃	C₂³	1	24	yes	—
46	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	—
47	C₃×C₄×C₃⋊D₃	C₂³	1	24	yes	—
48	C₃×#634	C₂³	1	12	yes	—
49	C₃×#634	C₂³	1	24	yes	—
50	C₂×C₃×2₋¹⁺⁴	—	9	1	no	—
51	C₂×#1010	—	3	4	no	—
52	C₃²×#41	—	2	32	no	—
53	C₃²×#41	C₂×D₃	1	32	yes	complemented
54	C₃²×#41	C₂²×C₃	1	8	yes	complemented
55	C₂×C₃²×Q₈	—	2	4	no	—
56	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
57	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃²×D₄	—	2	12	no	—
59	C₂×C₃²×D₄	C₂×D₃	1	12	yes	—
60	C₂×C₃²×D₄	C₂²×C₃	1	3	yes	—
61	C₂²×C₃²×C₄	—	2	12	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	12	yes	—
63	C₂²×C₃²×C₄	C₂²×C₃	1	3	yes	—
64	C₂×#638	C₂²×C₃	1	6	yes	—
65	C₂²×C₃⋊Dic₃	C₂²×C₃	1	6	yes	—
66	Q₈×C₃⋊D₃	C₂²×C₃	1	16	yes	complemented
67	#3830	C₂²×C₃	1	48	yes	complemented
68	#3828	C₂²×C₃	1	24	yes	complemented
69	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	6	yes	—
71	C₂×#634	C₂²×C₃	1	3	yes	—
72	C₂×#634	C₂²×C₃	1	6	yes	—
73	C₂×#634	C₂²×C₃	1	24	yes	complemented
74	C₂×C₃×#67	—	3	24	no	—
75	C₂²×C₃×Dic₃	—	3	24	no	—
76	C₃×D₃×Q₈	—	3	64	no	—
77	C₃×#237	—	3	192	no	—
78	C₃×#235	—	3	96	no	—
79	C₂×C₃×D₁₂	—	3	4	no	—
80	C₂×C₃×C₄×D₃	—	3	24	no	—
81	C₂×C₃×Dic₆	—	3	12	no	—
82	C₂×C₃×Dic₆	—	3	24	no	—
83	C₂×C₃×Dic₆	—	3	96	no	—
84	C₂²×C₃³	—	2	6	no	—
85	C₂²×C₃³	C₂⁴	1	6	yes	—
86	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
87	C₂×C₃×C₃⋊D₃	—	2	4	no	—
88	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
89	C₃³×C₄	C₂⁴	1	2	yes	—
90	C₃³×C₄	C₂⁴	1	6	yes	—
91	C₃×C₃⋊Dic₃	C₂⁴	1	12	yes	—
92	C₃×2₋¹⁺⁴	—	9	16	no	—
93	C₂×C₃×#41	—	2	4	no	—
94	C₂×C₃×#41	—	9	6	no	—
95	C₂×C₃×#41	—	9	3	no	—
96	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
97	C₂×C₃×#41	C₃⋊D₃	1	1	yes	characteristic, complemented
98	C₂²×C₃×Q₈	—	9	2	no	—
99	C₂²×C₃×Q₈	—	9	3	no	—
100	#1010	—	3	64	no	—
101	C₂×D₃×Q₈	—	3	8	no	—
102	C₂×#237	—	3	24	no	—
103	C₂×#235	—	3	12	no	—
104	C₂²×Dic₆	—	3	12	no	—
105	C₂³×C₃²	—	2	12	no	—
106	C₂³×C₃²	C₂²×D₃	1	12	yes	—
107	C₂³×C₃²	C₂³×C₃	1	3	yes	—
108	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
109	C₂²×C₃×D₃	—	3	8	no	—
110	C₃²×Q₈	—	2	16	no	—
111	C₃²×Q₈	C₂²×D₃	1	16	yes	—
112	C₃²×Q₈	C₂³×C₃	1	4	yes	—
113	C₃²×D₄	—	2	48	no	—
114	C₃²×D₄	C₂²×D₃	1	48	yes	—
115	C₃²×D₄	C₂³×C₃	1	12	yes	—
116	C₂×C₃²×C₄	—	2	4	no	—
117	C₂×C₃²×C₄	—	2	12	no	—
118	C₂×C₃²×C₄	—	2	48	no	—
119	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
120	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	—
121	C₂×C₃²×C₄	C₂²×D₃	1	48	yes	—
122	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂³×C₃	1	3	yes	—
124	C₂×C₃²×C₄	C₂³×C₃	1	12	yes	—
125	#638	C₂³×C₃	1	24	yes	—
126	C₂×C₃⋊Dic₃	C₂³×C₃	1	6	yes	—
127	C₂×C₃⋊Dic₃	C₂³×C₃	1	24	yes	—
128	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	—
129	C₄×C₃⋊D₃	C₂³×C₃	1	24	yes	—
130	#634	C₂³×C₃	1	12	yes	—
131	#634	C₂³×C₃	1	24	yes	—
132	C₃×#67	—	3	96	no	—
133	C₂×C₃×Dic₃	—	3	24	no	—
134	C₂×C₃×Dic₃	—	3	96	no	—
135	C₃×D₁₂	—	3	16	no	—
136	C₃×C₄×D₃	—	3	96	no	—
137	C₃×Dic₆	—	3	48	no	—
138	C₃×Dic₆	—	3	96	no	—
139	C₂×2₋¹⁺⁴	—	9	1	no	Sylow
140	C₂×C₃³	—	2	6	no	—
141	C₂×C₃³	2₋¹⁺⁴	1	2	yes	complemented
142	C₂×C₃³	C₂⁵	1	1	yes	characteristic
143	C₃×C₃⋊D₃	—	2	4	no	—
144	C₃×#41	—	2	32	no	—
145	C₃×#41	—	9	48	no	—
146	C₃×#41	—	9	24	no	—
147	C₃×#41	C₂×C₃×D₃	1	32	yes	complemented
148	C₃×#41	C₂×C₃⋊D₃	1	8	yes	complemented
149	C₂×C₃×Q₈	—	2	4	no	—
150	C₂×C₃×Q₈	—	9	16	no	—
151	C₂×C₃×Q₈	—	9	6	no	—
152	C₂×C₃×Q₈	—	9	3	no	—
153	C₂×C₃×Q₈	—	9	24	no	—
154	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
155	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
156	C₂×C₃×D₄	—	2	12	no	—
157	C₂×C₃×D₄	—	9	6	no	—
158	C₂×C₃×D₄	—	9	1	no	—
159	C₂×C₃×D₄	C₂×C₃×D₃	1	12	yes	—
160	C₂×C₃×D₄	C₂×C₃⋊D₃	1	3	yes	—
161	C₂²×C₃×C₄	—	2	12	no	—
162	C₂²×C₃×C₄	—	9	6	no	—
163	C₂²×C₃×C₄	—	9	6	no	—
164	C₂²×C₃×C₄	C₂×C₃×D₃	1	12	yes	—
165	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	3	yes	—
166	C₂×#67	—	3	24	no	—
167	C₂²×Dic₃	—	3	24	no	—
168	D₃×Q₈	—	3	64	no	—
169	#237	—	3	192	no	—
170	#235	—	3	96	no	—
171	C₂×D₁₂	—	3	4	no	—
172	C₂×C₄×D₃	—	3	24	no	—
173	C₂×Dic₆	—	3	12	no	—
174	C₂×Dic₆	—	3	24	no	—
175	C₂×Dic₆	—	3	96	no	—
176	C₂²×C₃²	—	2	6	no	—
177	C₂²×C₃²	—	2	4	no	—
178	C₂²×C₃²	—	2	24	no	—
179	C₂²×C₃²	—	2	24	no	—
180	C₂²×C₃²	—	4	24	no	—
181	C₂²×C₃²	C₂³×D₃	1	24	yes	—
182	C₂²×C₃²	C₂³×D₃	1	4	yes	—
183	C₂²×C₃²	C₂⁴×C₃	1	6	yes	—
184	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
185	C₂×C₃⋊D₃	—	2	4	no	—
186	C₂×C₃⋊D₃	C₂⁴×C₃	1	4	yes	—
187	C₂×C₃×D₃	—	3	16	no	—
188	C₂×C₃×D₃	—	6	16	no	—
189	C₃²×C₄	—	2	8	no	—
190	C₃²×C₄	—	2	24	no	—
191	C₃²×C₄	C₂³×D₃	1	8	yes	—
192	C₃²×C₄	C₂³×D₃	1	24	yes	—
193	C₃²×C₄	C₂⁴×C₃	1	2	yes	—
194	C₃²×C₄	C₂⁴×C₃	1	6	yes	—
195	C₃⋊Dic₃	C₂⁴×C₃	1	12	yes	—
196	C₃×Dic₃	—	3	48	no	—
197	2₋¹⁺⁴	—	9	16	no	—
198	C₂×#41	—	9	6	no	—
199	C₂×#41	—	9	3	no	—
200	C₂×#41	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
201	C₂²×Q₈	—	9	2	no	—
202	C₂²×Q₈	—	9	3	no	—
203	C₃³	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
204	C₂³×C₃	—	2	12	no	—
205	C₂³×C₃	—	9	2	no	—
206	C₂³×C₃	C₂²×C₃×D₃	1	12	yes	—
207	C₂³×C₃	C₂²×C₃⋊D₃	1	3	yes	—
208	C₂²×D₃	—	3	8	no	—
209	C₃×Q₈	—	2	16	no	—
210	C₃×Q₈	—	9	24	no	—
211	C₃×Q₈	—	9	12	no	—
212	C₃×Q₈	C₂²×C₃×D₃	1	16	yes	—
213	C₃×Q₈	C₂²×C₃⋊D₃	1	4	yes	—
214	C₃×D₄	—	2	48	no	—
215	C₃×D₄	—	9	24	no	—
216	C₃×D₄	—	9	4	no	—
217	C₃×D₄	C₂²×C₃×D₃	1	48	yes	—
218	C₃×D₄	C₂²×C₃⋊D₃	1	12	yes	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	12	no	—
221	C₂×C₃×C₄	—	2	48	no	—
222	C₂×C₃×C₄	—	9	24	no	—
223	C₂×C₃×C₄	—	9	6	no	—
224	C₂×C₃×C₄	—	9	24	no	—
225	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
226	C₂×C₃×C₄	C₂²×C₃×D₃	1	12	yes	—
227	C₂×C₃×C₄	C₂²×C₃×D₃	1	48	yes	—
228	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	12	yes	—
229	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	3	yes	—
230	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
231	#67	—	3	96	no	—
232	C₂×Dic₃	—	3	24	no	—
233	C₂×Dic₃	—	3	96	no	—
234	D₁₂	—	3	16	no	—
235	C₄×D₃	—	3	96	no	—
236	Dic₆	—	3	48	no	—
237	Dic₆	—	3	96	no	—
238	C₂×C₃²	—	2	6	no	—
239	C₂×C₃²	—	2	8	no	—
240	C₂×C₃²	—	2	4	no	—
241	C₂×C₃²	—	2	24	no	—
242	C₂×C₃²	—	4	24	no	—
243	C₂×C₃²	#1010	1	8	yes	complemented
244	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	complemented
245	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
246	C₂×C₃²	C₂⁵×C₃	1	1	yes	characteristic
247	C₃⋊D₃	—	2	4	no	—
248	C₃×D₃	—	6	16	no	—
249	#41	—	9	48	no	—
250	#41	—	9	24	no	—
251	#41	C₂×C₃×C₃⋊D₃	1	8	yes	complemented
252	C₂×Q₈	—	9	16	no	—
253	C₂×Q₈	—	9	6	no	—
254	C₂×Q₈	—	9	3	no	—
255	C₂×Q₈	—	9	24	no	—
256	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
257	C₂×D₄	—	9	6	no	—
258	C₂×D₄	—	9	1	no	—
259	C₂×D₄	C₂×C₃×C₃⋊D₃	1	3	yes	—
260	C₂²×C₄	—	9	6	no	—
261	C₂²×C₄	—	9	6	no	—
262	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	3	yes	—
263	C₂²×C₃	—	2	24	no	—
264	C₂²×C₃	—	2	6	no	—
265	C₂²×C₃	—	2	4	no	—
266	C₂²×C₃	—	2	24	no	—
267	C₂²×C₃	—	4	24	no	—
268	C₂²×C₃	—	9	4	no	—
269	C₂²×C₃	—	18	4	no	—
270	C₂²×C₃	C₂³×C₃×D₃	1	24	yes	—
271	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
272	C₂²×C₃	C₂³×C₃⋊D₃	1	6	yes	—
273	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
274	C₂×D₃	—	3	16	no	—
275	C₂×D₃	—	6	16	no	—
276	C₃×C₄	—	2	8	no	—
277	C₃×C₄	—	2	24	no	—
278	C₃×C₄	—	9	12	no	—
279	C₃×C₄	C₂³×C₃×D₃	1	8	yes	—
280	C₃×C₄	C₂³×C₃×D₃	1	24	yes	—
281	C₃×C₄	C₂³×C₃⋊D₃	1	6	yes	—
282	C₃×C₄	C₂³×C₃⋊D₃	1	2	yes	—
283	Dic₃	—	3	48	no	—
284	C₃²	—	2	4	no	—
285	C₃²	C₂×#1010	1	4	yes	complemented
286	C₃²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic, complemented
287	C₂³	—	9	2	no	—
288	C₂³	C₂²×C₃×C₃⋊D₃	1	3	yes	—
289	Q₈	—	9	24	no	—
290	Q₈	—	9	12	no	—
291	Q₈	C₂²×C₃×C₃⋊D₃	1	4	yes	—
292	D₄	—	9	24	no	—
293	D₄	—	9	4	no	—
294	D₄	C₂²×C₃×C₃⋊D₃	1	12	yes	—
295	C₂×C₄	—	9	6	no	—
296	C₂×C₄	—	9	24	no	—
297	C₂×C₄	—	9	24	no	—
298	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	3	yes	—
299	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
300	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	12	yes	—
301	C₂×C₃	—	2	24	no	—
302	C₂×C₃	—	2	6	no	—
303	C₂×C₃	—	2	8	no	—
304	C₂×C₃	—	2	4	no	—
305	C₂×C₃	—	4	24	no	—
306	C₂×C₃	—	18	4	no	—
307	C₂×C₃	C₃×#1010	1	8	yes	complemented
308	C₂×C₃	#64367	1	2	yes	direct product factor
309	C₂×C₃	C₂⁴×C₃×D₃	1	4	yes	—
310	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
311	D₃	—	6	16	no	—
312	C₂²	—	2	6	no	—
313	C₂²	—	9	4	no	—
314	C₂²	—	18	4	no	—
315	C₂²	C₂³×C₃×C₃⋊D₃	1	6	yes	—
316	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
317	C₄	—	9	12	no	—
318	C₄	C₂³×C₃×C₃⋊D₃	1	6	yes	—
319	C₄	C₂³×C₃×C₃⋊D₃	1	2	yes	—
320	C₃	—	2	4	no	—
321	C₃	C₂×C₃×#1010	1	4	yes	complemented
322	C₃	C₂×#64367	1	1	yes	characteristic, direct product factor
323	C₂	—	2	6	no	—
324	C₂	—	18	4	no	—
325	C₂	C₃×#64367	1	2	yes	direct product factor
326	C₂	C₂⁴×C₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂×C₃²	C₂⁵×C₃
Frattini	C₂	C₂⁴×C₃×C₃⋊D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃×#41	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×2₋¹⁺⁴
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₃×#64367	C₂	direct (N × H)
3. C₂×C₃×Q₈×C₃⋊D₃	C₂	semidirect
4. C₂×C₃×#3830	C₂	semidirect
5. C₂×C₃×#3828	C₂	semidirect
6. C₂²×C₃×#634	C₂	semidirect
7. C₂×#64367	C₃	direct (N × H)
9. C₃³×#41	C₂²	semidirect
15. C₃×Q₈×C₃⋊D₃	C₂²	semidirect
16. C₃×#3830	C₂²	semidirect
17. C₃×#3828	C₂²	semidirect
22. C₂×C₃×#634	C₂²	semidirect
24. C₂×C₃²×#41	D₃	semidirect
25. C₂×C₃²×#41	C₂×C₃	semidirect
26. #64367	C₂×C₃	direct (N × H)
27. C₂×Q₈×C₃⋊D₃	C₂×C₃	semidirect
28. C₂×#3830	C₂×C₃	semidirect
29. C₂×#3828	C₂×C₃	semidirect
30. C₂²×#634	C₂×C₃	semidirect
53. C₃²×#41	C₂×D₃	semidirect
54. C₃²×#41	C₂²×C₃	semidirect
66. Q₈×C₃⋊D₃	C₂²×C₃	semidirect
67. #3830	C₂²×C₃	semidirect
68. #3828	C₂²×C₃	semidirect
73. C₂×#634	C₂²×C₃	semidirect
96. C₂×C₃×#41	C₃×D₃	semidirect
97. C₂×C₃×#41	C₃⋊D₃	semidirect
141. C₂×C₃³	2₋¹⁺⁴	semidirect
147. C₃×#41	C₂×C₃×D₃	semidirect
148. C₃×#41	C₂×C₃⋊D₃	semidirect
200. C₂×#41	C₃×C₃⋊D₃	semidirect
203. C₃³	C₂×2₋¹⁺⁴	semidirect
243. C₂×C₃²	#1010	semidirect
244. C₂×C₃²	C₃×2₋¹⁺⁴	semidirect
251. #41	C₂×C₃×C₃⋊D₃	semidirect
285. C₃²	C₂×#1010	semidirect
286. C₃²	C₂×C₃×2₋¹⁺⁴	semidirect
307. C₂×C₃	C₃×#1010	semidirect
308. C₂×C₃	#64367	direct (N × H)
321. C₃	C₂×C₃×#1010	semidirect
322. C₃	C₂×#64367	direct (N × H)
325. C₂	C₃×#64367	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×#41	2
C₃×#64367	2
C₂×C₃×Q₈×C₃⋊D₃	2
C₂×C₃×#3830	2
C₂×C₃×#3828	2
C₂²×C₃×#634	2
C₂×#64367	3
C₂×C₃×#1010	3

Subgroups — C2×C3×#64367 #13181742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64367 #13181742