Subgroups — C₂×C₃×#63636 #13163022

Order 1728.

1580 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63636	C₂	1	4	yes	maximal, direct product factor
5	C₂×#63636	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×#809	—	3	4	no	maximal
7	C₂³×C₃×C₃⋊D₃	—	2	1	no	—
8	C₂²×C₃³×C₄	—	2	1	no	—
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
11	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
12	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	4	yes	complemented
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₃³×C₄⋊C₄	—	2	1	no	—
15	C₃³×C₄⋊C₄	C₂²	1	2	yes	complemented
16	C₂×C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
17	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
18	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×D₁₂	—	3	4	no	—
20	C₂×C₃²×C₄⋊C₄	—	2	4	no	—
21	C₂×C₃²×C₄⋊C₄	D₃	1	4	yes	complemented
22	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂²×C₃⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₃⋊C₈	—	3	4	no	—
25	#63636	C₂×C₃	1	4	yes	direct product factor
26	C₃×#809	—	3	16	no	—
27	C₂³×C₃³	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
29	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
30	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
31	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
32	C₂×C₃³×C₄	—	2	2	no	—
33	C₂×C₃³×C₄	—	4	2	no	—
34	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
35	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
36	C₂×C₃³×C₄	D₄	1	2	yes	—
37	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
38	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
39	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
40	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
41	C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
42	C₂×C₃×#102	—	9	1	no	—
43	C₂×#809	—	3	4	no	—
44	C₂³×C₃⋊D₃	—	2	1	no	—
45	C₂³×C₃×D₃	—	6	4	no	—
46	C₂²×C₃²×C₄	—	2	4	no	—
47	C₂²×C₃²×C₄	—	2	8	no	—
48	C₂²×C₃²×C₄	—	2	4	no	—
49	C₂²×C₃²×C₄	—	2	1	no	—
50	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
51	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
53	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
54	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	4	yes	complemented
55	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
56	C₂×C₃×D₁₂	—	3	16	no	—
57	C₂×C₃×D₁₂	—	3	8	no	—
58	C₂×C₃×D₁₂	—	6	8	no	—
59	C₂×C₃×D₁₂	—	6	4	no	—
60	C₃²×C₄⋊C₄	—	2	8	no	—
61	C₃²×C₄⋊C₄	—	2	8	no	—
62	C₃²×C₄⋊C₄	—	2	4	no	—
63	C₃²×C₄⋊C₄	—	2	1	no	—
64	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
65	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
66	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
67	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
68	C₂×C₃×C₃⋊C₈	—	3	8	no	—
69	C₂×C₃×C₃⋊C₈	—	6	8	no	—
70	C₂²×C₃³	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₃³	D₈	1	2	yes	—
72	C₂²×C₃³	SD₁₆	1	2	yes	—
73	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
74	C₂×C₃×C₃⋊D₃	—	2	4	no	—
75	C₂×C₃×C₃⋊D₃	—	4	8	no	—
76	C₂×C₃×C₃⋊D₃	—	4	2	no	—
77	C₂×C₃×C₃⋊D₃	—	4	2	no	—
78	C₃³×C₄	—	4	2	no	—
79	C₃³×C₄	C₂²⋊C₄	1	2	yes	—
80	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
81	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₃×D₄	—	9	1	no	—
83	C₂²×D₁₂	—	3	4	no	—
84	C₂²×C₃×C₈	—	9	1	no	—
85	C₂×C₃×C₄⋊C₄	—	2	4	no	—
86	C₂×C₃×C₄⋊C₄	C₃×D₃	1	4	yes	complemented
87	C₂×C₃×C₄⋊C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
88	C₂²×C₃⋊C₈	—	3	4	no	—
89	C₃×#102	—	9	4	no	—
90	#809	—	3	16	no	—
91	C₂³×C₃²	—	2	4	no	—
92	C₂³×C₃²	#67	1	4	yes	—
93	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
94	C₂²×C₃⋊D₃	—	2	4	no	—
95	C₂²×C₃⋊D₃	—	2	2	no	—
96	C₂²×C₃⋊D₃	—	4	2	no	—
97	C₂²×C₃⋊D₃	—	4	2	no	—
98	C₂²×C₃×D₃	—	6	16	no	—
99	C₂²×C₃×D₃	—	6	8	no	—
100	C₂²×C₃×D₃	—	12	8	no	—
101	C₂²×C₃×D₃	—	12	8	no	—
102	C₂×C₃²×C₄	—	2	16	no	—
103	C₂×C₃²×C₄	—	2	8	no	—
104	C₂×C₃²×C₄	—	2	2	no	—
105	C₂×C₃²×C₄	—	2	8	no	—
106	C₂×C₃²×C₄	—	2	8	no	—
107	C₂×C₃²×C₄	—	2	4	no	—
108	C₂×C₃²×C₄	—	2	4	no	—
109	C₂×C₃²×C₄	—	4	16	no	—
110	C₂×C₃²×C₄	—	4	8	no	—
111	C₂×C₃²×C₄	—	4	2	no	—
112	C₂×C₃²×C₄	C₄×D₃	1	8	yes	—
113	C₂×C₃²×C₄	D₁₂	1	8	yes	—
114	C₂×C₃²×C₄	#67	1	4	yes	—
115	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
116	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
117	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
119	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
120	C₄⋊(C₃⋊D₃)	—	2	4	no	—
121	C₄⋊(C₃⋊D₃)	—	2	2	no	—
122	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	4	yes	complemented
123	C₃×D₁₂	—	3	16	no	—
124	C₃×D₁₂	—	6	16	no	—
125	C₃×D₁₂	—	6	8	no	—
126	C₃⋊(C₃⋊C₈)	—	2	2	no	—
127	C₃×C₃⋊C₈	—	6	8	no	—
128	C₂×#102	—	9	1	no	Sylow
129	C₂×C₃³	#102	1	4	yes	complemented
130	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₃³	C₂×D₈	1	1	yes	characteristic
132	C₂×C₃³	C₂×SD₁₆	1	1	yes	characteristic
133	C₃×C₃⋊D₃	—	4	4	no	—
134	C₂⁴×C₃	—	18	1	no	—
135	C₂³×D₃	—	6	4	no	—
136	C₂×C₃×D₄	—	9	4	no	—
137	C₂×C₃×D₄	—	9	2	no	—
138	C₂×C₃×D₄	—	18	2	no	—
139	C₂×C₃×D₄	—	18	1	no	—
140	C₂²×C₃×C₄	—	2	8	no	—
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	4	no	—
144	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
145	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
146	C₂×D₁₂	—	3	16	no	—
147	C₂×D₁₂	—	3	8	no	—
148	C₂×D₁₂	—	6	8	no	—
149	C₂×D₁₂	—	6	4	no	—
150	C₂×C₃×C₈	—	9	2	no	—
151	C₂×C₃×C₈	—	18	2	no	—
152	C₃×C₄⋊C₄	—	2	8	no	—
153	C₃×C₄⋊C₄	—	2	4	no	—
154	C₃×C₄⋊C₄	—	2	1	no	—
155	C₃×C₄⋊C₄	—	2	8	no	—
156	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
157	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	complemented
158	C₂×C₃⋊C₈	—	3	8	no	—
159	C₂×C₃⋊C₈	—	6	8	no	—
160	C₂²×C₃²	—	2	8	no	—
161	C₂²×C₃²	—	2	8	no	—
162	C₂²×C₃²	—	2	8	no	—
163	C₂²×C₃²	—	2	4	no	—
164	C₂²×C₃²	(C₂×D₃)⋊C₄	1	8	yes	—
165	C₂²×C₃²	#213	1	8	yes	—
166	C₂²×C₃²	#215	1	8	yes	—
167	C₂²×C₃²	C₃×C₂²⋊C₄	1	2	yes	—
168	C₂²×C₃²	C₃×D₈	1	2	yes	—
169	C₂²×C₃²	C₃×SD₁₆	1	2	yes	—
170	C₂²×C₃²	C₂×#67	1	4	yes	—
171	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
172	C₂×C₃⋊D₃	—	2	4	no	—
173	C₂×C₃⋊D₃	—	4	8	no	—
174	C₂×C₃⋊D₃	—	4	2	no	—
175	C₂×C₃⋊D₃	—	4	2	no	—
176	C₂×C₃×D₃	—	6	16	no	—
177	C₂×C₃×D₃	—	12	32	no	—
178	C₂×C₃×D₃	—	12	8	no	—
179	C₂×C₃×D₃	—	12	8	no	—
180	C₃²×C₄	—	2	8	no	—
181	C₃²×C₄	—	2	4	no	—
182	C₃²×C₄	—	2	4	no	—
183	C₃²×C₄	—	4	16	no	—
184	C₃²×C₄	—	4	8	no	—
185	C₃²×C₄	—	4	2	no	—
186	C₃²×C₄	(C₂×D₃)⋊C₄	1	8	yes	—
187	C₃²×C₄	C₃×C₂²⋊C₄	1	2	yes	—
188	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
189	C₃²×C₄	C₂×D₁₂	1	4	yes	—
190	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
191	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂²×D₄	—	9	1	no	—
193	C₂²×C₈	—	9	1	no	—
194	C₂×C₄⋊C₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
195	#102	—	9	4	no	—
196	C₃³	C₂×#102	1	1	yes	characteristic, complemented, Sylow
197	C₂³×C₃	—	2	4	no	—
198	C₂³×C₃	—	18	4	no	—
199	C₂³×C₃	—	18	2	no	—
200	C₂³×C₃	—	36	2	no	—
201	C₂³×C₃	—	36	2	no	—
202	C₂³×C₃	C₃×#67	1	4	yes	—
203	C₂³×C₃	#638	1	1	yes	characteristic
204	C₂²×D₃	—	6	16	no	—
205	C₂²×D₃	—	6	8	no	—
206	C₂²×D₃	—	12	8	no	—
207	C₂²×D₃	—	12	8	no	—
208	C₃×D₄	—	9	4	no	—
209	C₃×D₄	—	18	4	no	—
210	C₃×D₄	—	18	2	no	—
211	C₂×C₃×C₄	—	2	16	no	—
212	C₂×C₃×C₄	—	2	8	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	8	no	—
215	C₂×C₃×C₄	—	2	8	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	4	no	—
218	C₂×C₃×C₄	—	4	16	no	—
219	C₂×C₃×C₄	—	4	8	no	—
220	C₂×C₃×C₄	—	4	2	no	—
221	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
222	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
223	C₂×C₃×C₄	C₃×#67	1	4	yes	—
224	C₂×C₃×C₄	C₄×C₃⋊D₃	1	2	yes	—
225	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
226	C₂×C₃×C₄	#638	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
228	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
229	D₁₂	—	3	16	no	—
230	D₁₂	—	6	16	no	—
231	D₁₂	—	6	8	no	—
232	C₃×C₈	—	18	2	no	—
233	C₃⋊C₈	—	6	8	no	—
234	C₂×C₃²	—	2	4	no	—
235	C₂×C₃²	—	2	4	no	—
236	C₂×C₃²	—	2	4	no	—
237	C₂×C₃²	—	2	16	no	—
238	C₂×C₃²	#809	1	16	yes	complemented
239	C₂×C₃²	C₃×#102	1	4	yes	complemented
240	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
241	C₂×C₃²	C₂×#213	1	4	yes	—
242	C₂×C₃²	C₂×#215	1	4	yes	—
243	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
245	C₂×C₃²	C₂×C₃×SD₁₆	1	1	yes	characteristic
246	C₃⋊D₃	—	4	4	no	—
247	C₃×D₃	—	12	16	no	—
248	C₂⁴	—	18	1	no	—
249	C₂×D₄	—	9	4	no	—
250	C₂×D₄	—	9	2	no	—
251	C₂×D₄	—	18	2	no	—
252	C₂×D₄	—	18	1	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
255	C₂×C₈	—	9	2	no	—
256	C₂×C₈	—	18	2	no	—
257	C₄⋊C₄	—	2	1	no	—
258	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
259	C₂²×C₃	—	2	8	no	—
260	C₂²×C₃	—	2	8	no	—
261	C₂²×C₃	—	2	8	no	—
262	C₂²×C₃	—	2	4	no	—
263	C₂²×C₃	—	18	4	no	—
264	C₂²×C₃	—	36	2	no	—
265	C₂²×C₃	—	36	8	no	—
266	C₂²×C₃	—	36	2	no	—
267	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
268	C₂²×C₃	C₃×#213	1	8	yes	—
269	C₂²×C₃	C₃×#215	1	8	yes	—
270	C₂²×C₃	#3752	1	2	yes	—
271	C₂²×C₃	#3753	1	2	yes	—
272	C₂²×C₃	#3755	1	2	yes	—
273	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
274	C₂²×C₃	C₂×#638	1	1	yes	characteristic
275	C₂×D₃	—	6	16	no	—
276	C₂×D₃	—	12	8	no	—
277	C₂×D₃	—	12	8	no	—
278	C₂×D₃	—	12	32	no	—
279	C₃×C₄	—	2	8	no	—
280	C₃×C₄	—	2	4	no	—
281	C₃×C₄	—	2	4	no	—
282	C₃×C₄	—	4	16	no	—
283	C₃×C₄	—	4	8	no	—
284	C₃×C₄	—	4	2	no	—
285	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
286	C₃×C₄	#3752	1	2	yes	—
287	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
288	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
289	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
290	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
291	C₃²	—	2	4	no	—
292	C₃²	C₂×#809	1	4	yes	complemented
293	C₃²	C₂×C₃×#102	1	1	yes	characteristic, complemented
294	C₂³	—	18	4	no	—
295	C₂³	—	18	2	no	—
296	C₂³	—	36	2	no	—
297	C₂³	—	36	2	no	—
298	C₂³	C₃×#638	1	1	yes	characteristic
299	D₄	—	9	4	no	—
300	D₄	—	18	4	no	—
301	D₄	—	18	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
305	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
306	C₂×C₄	C₃×#638	1	1	yes	characteristic
307	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
308	C₈	—	18	2	no	—
309	C₂×C₃	—	2	4	no	—
310	C₂×C₃	—	2	4	no	—
311	C₂×C₃	—	2	4	no	—
312	C₂×C₃	—	2	16	no	—
313	C₂×C₃	—	36	4	no	—
314	C₂×C₃	C₃×#809	1	16	yes	complemented
315	C₂×C₃	#63636	1	4	yes	direct product factor
316	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
317	C₂×C₃	C₂×C₃×#213	1	4	yes	—
318	C₂×C₃	C₂×C₃×#215	1	4	yes	—
319	C₂×C₃	C₂×#3752	1	1	yes	characteristic
320	C₂×C₃	C₂×#3753	1	1	yes	characteristic
321	C₂×C₃	C₂×#3755	1	1	yes	characteristic
322	D₃	—	12	16	no	—
323	C₂²	—	18	4	no	—
324	C₂²	—	36	2	no	—
325	C₂²	—	36	2	no	—
326	C₂²	—	36	8	no	—
327	C₂²	C₃×#3752	1	2	yes	—
328	C₂²	C₃×#3753	1	2	yes	—
329	C₂²	C₃×#3755	1	2	yes	—
330	C₂²	C₂×C₃×#638	1	1	yes	characteristic
331	C₄	—	4	2	no	—
332	C₄	C₃×#3752	1	2	yes	—
333	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
334	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
335	C₃	—	2	4	no	—
336	C₃	C₂×C₃×#809	1	4	yes	complemented
337	C₃	C₂×#63636	1	1	yes	characteristic, direct product factor
338	C₂	—	36	4	no	—
339	C₂	C₃×#63636	1	4	yes	direct product factor
340	C₂	C₂×C₃×#3752	1	1	yes	characteristic
341	C₂	C₂×C₃×#3753	1	1	yes	characteristic
342	C₂	C₂×C₃×#3755	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	#638
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₂×C₃³×C₄⋊C₄	C₂
socle	C₂³×C₃³	D₄
prime radical	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#102
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×C₄⋊C₄	C₂	semidirect
3. C₂²×C₃×C₃⋊(C₃⋊C₈)	C₂	semidirect
4. C₃×#63636	C₂	direct (N × H)
5. C₂×#63636	C₃	direct (N × H)
12. C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	semidirect
15. C₃³×C₄⋊C₄	C₂²	semidirect
17. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
21. C₂×C₃²×C₄⋊C₄	D₃	semidirect
22. C₂×C₃²×C₄⋊C₄	C₂×C₃	semidirect
23. C₂²×C₃⋊(C₃⋊C₈)	C₂×C₃	semidirect
25. #63636	C₂×C₃	direct (N × H)
40. C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	semidirect
54. C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	semidirect
64. C₃²×C₄⋊C₄	C₂×D₃	semidirect
65. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
67. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
86. C₂×C₃×C₄⋊C₄	C₃×D₃	semidirect
87. C₂×C₃×C₄⋊C₄	C₃⋊D₃	semidirect
122. C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	semidirect
129. C₂×C₃³	#102	semidirect
156. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
157. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
194. C₂×C₄⋊C₄	C₃×C₃⋊D₃	semidirect
196. C₃³	C₂×#102	semidirect
238. C₂×C₃²	#809	semidirect
239. C₂×C₃²	C₃×#102	semidirect
258. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
292. C₃²	C₂×#809	semidirect
293. C₃²	C₂×C₃×#102	semidirect
314. C₂×C₃	C₃×#809	semidirect
315. C₂×C₃	#63636	direct (N × H)
336. C₃	C₂×C₃×#809	semidirect
337. C₃	C₂×#63636	direct (N × H)
339. C₂	C₃×#63636	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×C₄⋊(C₃⋊D₃)	2
C₂×C₃³×C₄⋊C₄	2
C₂²×C₃×C₃⋊(C₃⋊C₈)	2
C₃×#63636	2
C₂×#63636	3
C₂×C₃×#809	3

Subgroups — C2×C3×#63636 #13163022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63636 #13163022