Subgroups — C₂×H(3,𝔽₃)×#121 #13154549

Order 1728.

2343 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×H(3,𝔽₃)	C₂	1	2	yes	maximal, complemented
3	C₂³×C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	H(3,𝔽₃)×#121	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂²⋊C₄×H(3,𝔽₃)	C₂	1	2	yes	maximal, complemented
7	C₂×C₃²×#121	C₃	1	4	yes	maximal, complemented
8	C₂⁴×H(3,𝔽₃)	C₂²	1	2	yes	—
9	C₂⁴×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
10	C₂×D₄×H(3,𝔽₃)	—	2	8	no	—
11	C₂×D₄×H(3,𝔽₃)	—	2	4	no	—
12	C₂×D₄×H(3,𝔽₃)	C₂²	1	8	yes	complemented
13	C₂×D₄×H(3,𝔽₃)	C₂²	1	4	yes	complemented
14	C₂²×C₄×H(3,𝔽₃)	—	2	4	no	—
15	C₂²×C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
16	C₂²×C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
17	C₂²×C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
18	C₂²×C₄×H(3,𝔽₃)	C₂²	1	4	yes	complemented
19	C₄⋊C₄×H(3,𝔽₃)	C₂²	1	4	yes	complemented
20	C₂²⋊C₄×H(3,𝔽₃)	C₂²	1	8	yes	complemented
21	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
22	C₂²×C₃²×D₄	C₂×C₃	1	8	yes	complemented
23	C₂³×C₃²×C₄	C₂×C₃	1	4	yes	complemented
24	C₃²×#121	C₂×C₃	1	32	yes	complemented
25	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	4	yes	complemented
26	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	8	yes	complemented
27	C₂³×H(3,𝔽₃)	—	2	2	no	—
28	C₂³×H(3,𝔽₃)	—	2	2	no	—
29	C₂³×H(3,𝔽₃)	—	2	4	no	—
30	C₂³×H(3,𝔽₃)	—	2	4	no	—
31	C₂³×H(3,𝔽₃)	—	2	4	no	—
32	C₂³×H(3,𝔽₃)	D₄	1	4	yes	complemented
33	C₂³×H(3,𝔽₃)	C₂³	1	4	yes	—
34	C₂³×H(3,𝔽₃)	C₂³	1	2	yes	—
35	C₂³×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
36	D₄×H(3,𝔽₃)	—	2	16	no	—
37	D₄×H(3,𝔽₃)	—	2	8	no	—
38	C₂×C₄×H(3,𝔽₃)	—	2	2	no	—
39	C₂×C₄×H(3,𝔽₃)	—	2	4	no	—
40	C₂×C₄×H(3,𝔽₃)	—	2	8	no	—
41	C₂×C₄×H(3,𝔽₃)	D₄	1	4	yes	complemented
42	C₂×C₄×H(3,𝔽₃)	C₂³	1	2	yes	—
43	C₂×C₄×H(3,𝔽₃)	C₂³	1	4	yes	—
44	C₂×C₄×H(3,𝔽₃)	C₂³	1	2	yes	—
45	C₂×C₃×#121	—	3	4	no	—
46	C₂×C₃×#121	C₃²	1	1	yes	characteristic
47	C₂⁴×C₃²	C₂²×C₃	1	8	yes	—
48	C₂⁴×C₃²	C₂²×C₃	1	4	yes	—
49	C₂×C₃²×D₄	—	2	32	no	—
50	C₂×C₃²×D₄	—	2	16	no	—
51	C₂×C₃²×D₄	C₂²×C₃	1	32	yes	complemented
52	C₂×C₃²×D₄	C₂²×C₃	1	16	yes	complemented
53	C₂²×C₃²×C₄	—	2	16	no	—
54	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
55	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
56	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
57	C₂²×C₃²×C₄	C₂²×C₃	1	16	yes	complemented
58	C₃²×C₄⋊C₄	C₂²×C₃	1	16	yes	complemented
59	C₃²×C₂²⋊C₄	C₂²×C₃	1	32	yes	complemented
60	C₂²×H(3,𝔽₃)	—	2	8	no	—
61	C₂²×H(3,𝔽₃)	—	2	2	no	—
62	C₂²×H(3,𝔽₃)	—	2	2	no	—
63	C₂²×H(3,𝔽₃)	—	2	4	no	—
64	C₂²×H(3,𝔽₃)	—	2	4	no	—
65	C₂²×H(3,𝔽₃)	—	2	4	no	—
66	C₂²×H(3,𝔽₃)	—	4	8	no	—
67	C₂²×H(3,𝔽₃)	C₂×D₄	1	2	yes	—
68	C₂²×H(3,𝔽₃)	C₂×D₄	1	2	yes	—
69	C₂²×H(3,𝔽₃)	C₂×D₄	1	4	yes	complemented
70	C₂²×H(3,𝔽₃)	#41	1	2	yes	—
71	C₂²×H(3,𝔽₃)	C₂⁴	1	1	yes	characteristic
72	C₄×H(3,𝔽₃)	—	2	2	no	—
73	C₄×H(3,𝔽₃)	—	2	4	no	—
74	C₄×H(3,𝔽₃)	C₂×D₄	1	4	yes	complemented
75	C₂²×C₃×D₄	—	3	4	no	—
76	C₂²×C₃×D₄	—	3	8	no	—
77	C₂²×C₃×D₄	C₂×C₃²	1	2	yes	—
78	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic
79	C₂³×C₃×C₄	—	3	4	no	—
80	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
81	C₃×#121	—	3	32	no	—
82	C₃×#121	C₂×C₃²	1	8	yes	—
83	C₂×C₃×C₄⋊C₄	—	3	4	no	—
84	C₂×C₃×C₄⋊C₄	C₂×C₃²	1	1	yes	characteristic
85	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
86	C₂×C₃×C₂²⋊C₄	C₂×C₃²	1	2	yes	—
87	C₂³×C₃²	—	2	8	no	—
88	C₂³×C₃²	—	2	8	no	—
89	C₂³×C₃²	—	2	16	no	—
90	C₂³×C₃²	—	2	16	no	—
91	C₂³×C₃²	—	2	16	no	—
92	C₂³×C₃²	C₃×D₄	1	16	yes	complemented
93	C₂³×C₃²	C₂³×C₃	1	16	yes	—
94	C₂³×C₃²	C₂³×C₃	1	8	yes	—
95	C₂³×C₃²	C₂³×C₃	1	4	yes	—
96	C₃²×D₄	—	2	64	no	—
97	C₃²×D₄	—	2	32	no	—
98	C₂×C₃²×C₄	—	2	8	no	—
99	C₂×C₃²×C₄	—	2	16	no	—
100	C₂×C₃²×C₄	—	2	32	no	—
101	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
102	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
103	C₂×C₃²×C₄	C₂³×C₃	1	16	yes	—
104	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
105	C₂×#121	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
106	C₂×H(3,𝔽₃)	—	2	4	no	—
107	C₂×H(3,𝔽₃)	—	4	4	no	—
108	C₂×H(3,𝔽₃)	#121	1	4	yes	direct product factor
109	C₂×H(3,𝔽₃)	C₂²×D₄	1	1	yes	characteristic
110	C₂×H(3,𝔽₃)	C₂²×D₄	1	1	yes	characteristic
111	C₂×H(3,𝔽₃)	C₂×#41	1	1	yes	characteristic
112	C₂⁴×C₃	—	3	4	no	—
113	C₂⁴×C₃	—	3	8	no	—
114	C₂⁴×C₃	C₂²×C₃²	1	2	yes	—
115	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
116	C₂×C₃×D₄	—	2	8	no	—
117	C₂×C₃×D₄	—	2	4	no	—
118	C₂×C₃×D₄	—	3	16	no	—
119	C₂×C₃×D₄	—	3	32	no	—
120	C₂×C₃×D₄	—	6	16	no	—
121	C₂×C₃×D₄	—	6	32	no	—
122	C₂×C₃×D₄	C₂²×C₃²	1	8	yes	—
123	C₂×C₃×D₄	C₂²×C₃²	1	4	yes	—
124	C₂²×C₃×C₄	—	2	4	no	—
125	C₂²×C₃×C₄	—	3	4	no	—
126	C₂²×C₃×C₄	—	3	4	no	—
127	C₂²×C₃×C₄	—	3	8	no	—
128	C₂²×C₃×C₄	—	3	16	no	—
129	C₂²×C₃×C₄	—	6	16	no	—
130	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
131	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
132	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂²×C₃²	1	4	yes	—
134	C₃×C₄⋊C₄	—	3	16	no	—
135	C₃×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
136	C₃×C₂²⋊C₄	—	3	32	no	—
137	C₃×C₂²⋊C₄	C₂²×C₃²	1	8	yes	—
138	C₂²×C₃²	—	2	32	no	—
139	C₂²×C₃²	—	2	8	no	—
140	C₂²×C₃²	—	2	8	no	—
141	C₂²×C₃²	—	2	16	no	—
142	C₂²×C₃²	—	2	16	no	—
143	C₂²×C₃²	—	2	16	no	—
144	C₂²×C₃²	—	4	32	no	—
145	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
146	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
147	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	complemented
148	C₂²×C₃²	C₃×#41	1	8	yes	—
149	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
150	C₃²×C₄	—	2	8	no	—
151	C₃²×C₄	—	2	16	no	—
152	C₃²×C₄	C₂×C₃×D₄	1	16	yes	complemented
153	C₂²×D₄	C₂×H(3,𝔽₃)	1	2	yes	complemented
154	C₂²×D₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
155	C₂³×C₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
156	#121	C₂×H(3,𝔽₃)	1	8	yes	direct product factor
157	C₂×C₄⋊C₄	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
158	C₂×C₂²⋊C₄	C₂×H(3,𝔽₃)	1	2	yes	complemented
159	H(3,𝔽₃)	C₂×#121	1	1	yes	characteristic, direct product factor, Sylow
160	C₂³×C₃	—	2	2	no	—
161	C₂³×C₃	—	2	2	no	—
162	C₂³×C₃	—	2	4	no	—
163	C₂³×C₃	—	2	4	no	—
164	C₂³×C₃	—	2	4	no	—
165	C₂³×C₃	—	3	16	no	—
166	C₂³×C₃	—	3	4	no	—
167	C₂³×C₃	—	3	8	no	—
168	C₂³×C₃	—	3	16	no	—
169	C₂³×C₃	—	6	8	no	—
170	C₂³×C₃	—	6	8	no	—
171	C₂³×C₃	—	6	16	no	—
172	C₂³×C₃	—	6	16	no	—
173	C₂³×C₃	—	6	16	no	—
174	C₂³×C₃	C₃²×D₄	1	4	yes	—
175	C₂³×C₃	C₂³×C₃²	1	4	yes	—
176	C₂³×C₃	C₂³×C₃²	1	2	yes	—
177	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
178	C₃×D₄	—	2	16	no	—
179	C₃×D₄	—	2	8	no	—
180	C₃×D₄	—	6	32	no	—
181	C₃×D₄	—	6	64	no	—
182	C₂×C₃×C₄	—	2	2	no	—
183	C₂×C₃×C₄	—	2	4	no	—
184	C₂×C₃×C₄	—	2	8	no	—
185	C₂×C₃×C₄	—	3	16	no	—
186	C₂×C₃×C₄	—	3	8	no	—
187	C₂×C₃×C₄	—	3	8	no	—
188	C₂×C₃×C₄	—	3	16	no	—
189	C₂×C₃×C₄	—	6	32	no	—
190	C₂×C₃×C₄	—	6	8	no	—
191	C₂×C₃×C₄	—	6	16	no	—
192	C₂×C₃×C₄	C₃²×D₄	1	4	yes	—
193	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
194	C₂×C₃×C₄	C₂³×C₃²	1	4	yes	—
195	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
196	C₂×C₃²	—	2	16	no	—
197	C₂×C₃²	—	4	16	no	—
198	C₂×C₃²	C₃×#121	1	16	yes	complemented
199	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
200	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
201	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
202	C₂⁴	C₂²×H(3,𝔽₃)	1	2	yes	—
203	C₂⁴	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
204	C₂×D₄	—	2	8	no	—
205	C₂×D₄	—	2	4	no	—
206	C₂×D₄	C₂²×H(3,𝔽₃)	1	8	yes	complemented
207	C₂×D₄	C₂²×H(3,𝔽₃)	1	4	yes	complemented
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
210	C₂²×C₄	C₂²×H(3,𝔽₃)	1	2	yes	—
211	C₂²×C₄	C₂²×H(3,𝔽₃)	1	1	yes	characteristic
212	C₂²×C₄	C₂²×H(3,𝔽₃)	1	4	yes	complemented
213	C₄⋊C₄	C₂²×H(3,𝔽₃)	1	4	yes	complemented
214	C₂²⋊C₄	C₂²×H(3,𝔽₃)	1	8	yes	complemented
215	C₂²×C₃	—	2	2	no	—
216	C₂²×C₃	—	2	2	no	—
217	C₂²×C₃	—	2	8	no	—
218	C₂²×C₃	—	2	4	no	—
219	C₂²×C₃	—	2	4	no	—
220	C₂²×C₃	—	2	4	no	—
221	C₂²×C₃	—	3	4	no	—
222	C₂²×C₃	—	3	8	no	—
223	C₂²×C₃	—	3	8	no	—
224	C₂²×C₃	—	3	16	no	—
225	C₂²×C₃	—	3	8	no	—
226	C₂²×C₃	—	4	8	no	—
227	C₂²×C₃	—	6	8	no	—
228	C₂²×C₃	—	6	32	no	—
229	C₂²×C₃	—	6	8	no	—
230	C₂²×C₃	—	6	16	no	—
231	C₂²×C₃	—	6	16	no	—
232	C₂²×C₃	—	6	16	no	—
233	C₂²×C₃	—	12	32	no	—
234	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
235	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
236	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	—
237	C₂²×C₃	C₃²×#41	1	2	yes	—
238	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
239	C₃×C₄	—	2	2	no	—
240	C₃×C₄	—	2	4	no	—
241	C₃×C₄	—	3	16	no	—
242	C₃×C₄	—	6	8	no	—
243	C₃×C₄	—	6	16	no	—
244	C₃×C₄	C₂×C₃²×D₄	1	4	yes	—
245	C₃²	C₂×C₃×#121	1	4	yes	complemented
246	C₂³	—	2	2	no	—
247	C₂³	—	2	2	no	—
248	C₂³	—	2	4	no	—
249	C₂³	—	2	4	no	—
250	C₂³	—	2	4	no	—
251	C₂³	D₄×H(3,𝔽₃)	1	4	yes	complemented
252	C₂³	C₂³×H(3,𝔽₃)	1	4	yes	—
253	C₂³	C₂³×H(3,𝔽₃)	1	2	yes	—
254	C₂³	C₂³×H(3,𝔽₃)	1	1	yes	characteristic
255	D₄	—	2	16	no	—
256	D₄	—	2	8	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	D₄×H(3,𝔽₃)	1	4	yes	complemented
261	C₂×C₄	C₂³×H(3,𝔽₃)	1	2	yes	—
262	C₂×C₄	C₂³×H(3,𝔽₃)	1	4	yes	—
263	C₂×C₄	C₂³×H(3,𝔽₃)	1	2	yes	—
264	C₂×C₃	—	2	4	no	—
265	C₂×C₃	—	3	16	no	—
266	C₂×C₃	—	3	4	no	—
267	C₂×C₃	—	3	4	no	—
268	C₂×C₃	—	3	4	no	—
269	C₂×C₃	—	4	4	no	—
270	C₂×C₃	—	6	16	no	—
271	C₂×C₃	—	12	16	no	—
272	C₂×C₃	C₃²×#121	1	4	yes	—
273	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
274	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
275	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
276	C₂²	—	2	8	no	—
277	C₂²	—	2	2	no	—
278	C₂²	—	2	2	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	4	no	—
282	C₂²	—	4	8	no	—
283	C₂²	C₂×D₄×H(3,𝔽₃)	1	2	yes	—
284	C₂²	C₂×D₄×H(3,𝔽₃)	1	2	yes	—
285	C₂²	C₂×D₄×H(3,𝔽₃)	1	4	yes	complemented
286	C₂²	#41×H(3,𝔽₃)	1	2	yes	—
287	C₂²	C₂⁴×H(3,𝔽₃)	1	1	yes	characteristic
288	C₄	—	2	2	no	—
289	C₄	—	2	4	no	—
290	C₄	C₂×D₄×H(3,𝔽₃)	1	4	yes	complemented
291	C₃	—	3	4	no	—
292	C₃	C₂×C₃²×#121	1	1	yes	characteristic
293	C₂	—	2	4	no	—
294	C₂	—	4	4	no	—
295	C₂	H(3,𝔽₃)×#121	1	4	yes	direct product factor
296	C₂	C₂²×D₄×H(3,𝔽₃)	1	1	yes	characteristic
297	C₂	C₂²×D₄×H(3,𝔽₃)	1	1	yes	characteristic
298	C₂	C₂×#41×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂³×C₃²
commutator, Frattini, cosocle	C₂²×C₃	C₂⁴×C₃²
LCS	G ▷ C₂²×C₃ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×H(3,𝔽₃)	C₂	semidirect
2. C₂²×D₄×H(3,𝔽₃)	C₂	semidirect
3. C₂³×C₄×H(3,𝔽₃)	C₂	semidirect
4. H(3,𝔽₃)×#121	C₂	direct (N × H)
5. C₂×C₄⋊C₄×H(3,𝔽₃)	C₂	semidirect
6. C₂×C₂²⋊C₄×H(3,𝔽₃)	C₂	semidirect
7. C₂×C₃²×#121	C₃	semidirect
12. C₂×D₄×H(3,𝔽₃)	C₂²	semidirect
13. C₂×D₄×H(3,𝔽₃)	C₂²	semidirect
18. C₂²×C₄×H(3,𝔽₃)	C₂²	semidirect
19. C₄⋊C₄×H(3,𝔽₃)	C₂²	semidirect
20. C₂²⋊C₄×H(3,𝔽₃)	C₂²	semidirect
21. C₂²×C₃²×D₄	C₂×C₃	semidirect
22. C₂²×C₃²×D₄	C₂×C₃	semidirect
23. C₂³×C₃²×C₄	C₂×C₃	semidirect
24. C₃²×#121	C₂×C₃	semidirect
25. C₂×C₃²×C₄⋊C₄	C₂×C₃	semidirect
26. C₂×C₃²×C₂²⋊C₄	C₂×C₃	semidirect
32. C₂³×H(3,𝔽₃)	D₄	semidirect
41. C₂×C₄×H(3,𝔽₃)	D₄	semidirect
51. C₂×C₃²×D₄	C₂²×C₃	semidirect
52. C₂×C₃²×D₄	C₂²×C₃	semidirect
57. C₂²×C₃²×C₄	C₂²×C₃	semidirect
58. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
59. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
69. C₂²×H(3,𝔽₃)	C₂×D₄	semidirect
74. C₄×H(3,𝔽₃)	C₂×D₄	semidirect
92. C₂³×C₃²	C₃×D₄	semidirect
101. C₂×C₃²×C₄	C₃×D₄	semidirect
105. C₂×#121	H(3,𝔽₃)	direct (N × H)
108. C₂×H(3,𝔽₃)	#121	direct (N × H)
147. C₂²×C₃²	C₂×C₃×D₄	semidirect
152. C₃²×C₄	C₂×C₃×D₄	semidirect
153. C₂²×D₄	C₂×H(3,𝔽₃)	semidirect
154. C₂²×D₄	C₂×H(3,𝔽₃)	semidirect
155. C₂³×C₄	C₂×H(3,𝔽₃)	semidirect
156. #121	C₂×H(3,𝔽₃)	direct (N × H)
157. C₂×C₄⋊C₄	C₂×H(3,𝔽₃)	semidirect
158. C₂×C₂²⋊C₄	C₂×H(3,𝔽₃)	semidirect
159. H(3,𝔽₃)	C₂×#121	direct (N × H)
198. C₂×C₃²	C₃×#121	semidirect
206. C₂×D₄	C₂²×H(3,𝔽₃)	semidirect
207. C₂×D₄	C₂²×H(3,𝔽₃)	semidirect
212. C₂²×C₄	C₂²×H(3,𝔽₃)	semidirect
213. C₄⋊C₄	C₂²×H(3,𝔽₃)	semidirect
214. C₂²⋊C₄	C₂²×H(3,𝔽₃)	semidirect
245. C₃²	C₂×C₃×#121	semidirect
251. C₂³	D₄×H(3,𝔽₃)	semidirect
260. C₂×C₄	D₄×H(3,𝔽₃)	semidirect
285. C₂²	C₂×D₄×H(3,𝔽₃)	semidirect
290. C₄	C₂×D₄×H(3,𝔽₃)	semidirect
295. C₂	H(3,𝔽₃)×#121	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×D₄×H(3,𝔽₃)	2
C₂³×C₄×H(3,𝔽₃)	2
H(3,𝔽₃)×#121	2
C₂×C₄⋊C₄×H(3,𝔽₃)	2
C₂×C₂²⋊C₄×H(3,𝔽₃)	2
C₂×C₃²×#121	3

Subgroups — C2×H(3,𝔽3)×#121 #13154549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×H(3,𝔽₃)×#121 #13154549