Subgroups — C₂²×C₃×#3828 #13181733

Order 1728.

6284 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×C₃⋊D₃
commutator, cosocle	C₂×C₃²	C₂⁵×C₃
Frattini	C₂	C₂⁴×C₃×C₃⋊D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂³×C₃×C₄	C₃⋊D₃
hypocenter	C₃²	C₂²×C₃×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂³×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
2. C₂²×C₃×#638	C₂	semidirect
3. C₂×C₃×#3828	C₂	direct (N × H)
4. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
5. C₂²×C₃×C₄×C₃⋊D₃	C₂	semidirect
6. C₂²×C₃×#634	C₂	semidirect
7. C₂²×#3828	C₃	direct (N × H)
13. C₂²×C₃³×C₄	C₂²	semidirect
14. C₂×C₃×#638	C₂²	semidirect
16. C₃×#3828	C₂²	direct (N × H)
17. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
19. C₂×C₃×#634	C₂²	semidirect
21. C₂³×C₃²×C₄	D₃	semidirect
22. C₂³×C₃²×C₄	C₂×C₃	semidirect
23. C₂²×#638	C₂×C₃	semidirect
24. C₂×#3828	C₂×C₃	direct (N × H)
25. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
26. C₂²×C₄×C₃⋊D₃	C₂×C₃	semidirect
27. C₂²×#634	C₂×C₃	semidirect
40. C₂×C₃³×C₄	C₂³	semidirect
41. C₃×#638	C₂³	semidirect
43. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
44. C₃×C₄×C₃⋊D₃	C₂³	semidirect
45. C₃×#634	C₂³	semidirect
58. C₂²×C₃²×C₄	C₂×D₃	semidirect
61. C₂²×C₃²×C₄	C₂²×C₃	semidirect
62. C₂×#638	C₂²×C₃	semidirect
64. #3828	C₂²×C₃	direct (N × H)
65. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
66. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
67. C₂×#634	C₂²×C₃	semidirect
75. C₂²×C₃³	#41	semidirect
89. C₂³×C₃×C₄	C₃×D₃	semidirect
90. C₂³×C₃×C₄	C₃⋊D₃	semidirect
114. C₂×C₃²×C₄	C₂²×D₃	semidirect
117. C₂×C₃²×C₄	C₂³×C₃	semidirect
118. #638	C₂³×C₃	semidirect
120. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
121. C₄×C₃⋊D₃	C₂³×C₃	semidirect
122. #634	C₂³×C₃	semidirect
130. C₂×C₃³	C₂×#41	semidirect
149. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
152. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
165. C₂²×C₃²	#235	semidirect
166. C₂²×C₃²	C₃×#41	semidirect
188. C₂³×C₄	C₃×C₃⋊D₃	semidirect
189. C₃³	C₂²×#41	semidirect
213. C₂×C₃×C₄	C₂²×C₃×D₃	semidirect
216. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
227. C₂×C₃²	C₂×#235	semidirect
228. C₂×C₃²	C₂×C₃×#41	semidirect
243. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
252. C₂²×C₃	C₃×#235	semidirect
253. C₂²×C₃	#3828	direct (N × H)
269. C₃²	C₂²×#235	semidirect
270. C₃²	C₂²×C₃×#41	semidirect
283. C₂×C₄	C₂²×C₃×C₃⋊D₃	semidirect
290. C₂×C₃	C₂×C₃×#235	semidirect
291. C₂×C₃	C₂×#3828	direct (N × H)
298. C₂²	C₃×#3828	direct (N × H)
305. C₃	C₂²×C₃×#235	semidirect
306. C₃	C₂²×#3828	direct (N × H)
309. C₂	C₂×C₃×#3828	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃³×C₄	2
C₂²×C₃×#638	2
C₂×C₃×#3828	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₂²×C₃×C₄×C₃⋊D₃	2
C₂²×C₃×#634	2
C₂²×#3828	3
C₂²×C₃×#235	3

Subgroups — C22×C3×#3828 #13181733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#3828 #13181733