Subgroups — C₃×#10596237 #13179517

Order 1728.

1728 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64364	C₂	1	2	yes	maximal, complemented
2	C₂×C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64151	C₂	1	2	yes	maximal, complemented
4	C₃×#64128	C₂	1	2	yes	maximal, complemented
5	C₃×#64127	C₂	1	4	yes	maximal, complemented
6	C₃×Q₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
7	C₃×#64113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64110	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596237	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5766	—	3	4	no	maximal
11	C₂×C₃³×Q₈	C₂²	1	2	yes	—
12	C₃×#3832	—	2	2	no	—
13	C₃×#3832	C₂²	1	4	yes	—
14	C₃×Q₈×C₃⋊D₃	—	2	2	no	—
15	C₃×Q₈×C₃⋊D₃	C₂²	1	4	yes	—
16	C₃×#3828	—	2	4	no	—
17	C₃×#3828	C₂²	1	1	yes	characteristic
18	C₃×#3828	C₂²	1	2	yes	—
19	C₃³×Q₁₆	C₂²	1	2	yes	—
20	C₃³×Q₁₆	C₂²	1	2	yes	—
21	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
22	C₃×#3756	C₂²	1	4	yes	—
23	C₃×#3755	C₂²	1	4	yes	—
24	C₃×#3748	C₂²	1	1	yes	characteristic
25	C₃×#3746	C₂²	1	1	yes	characteristic
26	C₃×#3745	C₂²	1	1	yes	characteristic
27	C₃×#3744	C₂²	1	2	yes	—
28	C₃×#3743	C₂²	1	2	yes	—
29	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	—
30	#64364	C₂×C₃	1	2	yes	complemented
31	C₃×#1007	—	3	8	no	—
32	C₂×C₃²×Q₁₆	—	2	4	no	—
33	C₂×C₃²×Q₁₆	D₃	1	4	yes	complemented
34	C₂×C₃²×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
35	#64151	C₂×C₃	1	2	yes	complemented
36	#64128	C₂×C₃	1	2	yes	complemented
37	#64127	C₂×C₃	1	4	yes	complemented
38	Q₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
39	#64113	C₂×C₃	1	1	yes	characteristic, complemented
40	#64110	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#942	—	3	8	no	—
42	C₃×#919	—	3	8	no	—
43	C₃×#918	—	3	16	no	—
44	C₃×D₃×Q₁₆	—	3	8	no	—
45	C₃×#904	—	3	4	no	—
46	C₃×#901	—	3	4	no	—
47	C₃³×Q₈	—	2	2	no	—
48	C₃³×Q₈	C₂³	1	4	yes	—
49	C₂×C₃³×C₄	—	2	2	no	—
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₃×#638	—	2	2	no	—
52	C₃×#638	D₄	1	2	yes	—
53	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
54	C₃×C₄⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
55	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
56	C₃×C₄×C₃⋊D₃	—	2	4	no	—
57	C₃×C₄×C₃⋊D₃	—	2	2	no	—
58	C₃×C₄×C₃⋊D₃	—	2	4	no	—
59	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
60	C₃×#634	—	2	4	no	—
61	C₃×#634	D₄	1	1	yes	characteristic
62	C₃×#634	C₂³	1	2	yes	—
63	C₃³×C₈	C₂³	1	1	yes	characteristic
64	C₃³×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
66	C₃×#578	—	9	1	no	—
67	#5766	—	3	4	no	—
68	C₂×C₃²×Q₈	—	2	8	no	—
69	C₂×C₃²×Q₈	C₂×D₃	1	8	yes	—
70	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
71	#3832	—	2	2	no	—
72	#3832	C₂²×C₃	1	4	yes	—
73	Q₈×C₃⋊D₃	—	2	2	no	—
74	Q₈×C₃⋊D₃	C₂²×C₃	1	4	yes	—
75	#3828	—	2	4	no	—
76	#3828	C₂²×C₃	1	1	yes	characteristic
77	#3828	C₂²×C₃	1	2	yes	—
78	C₃×#239	—	3	16	no	—
79	C₃×#239	—	6	8	no	—
80	C₃×D₃×Q₈	—	3	16	no	—
81	C₃×D₃×Q₈	—	6	8	no	—
82	C₃×#235	—	3	4	no	—
83	C₃×#235	—	3	8	no	—
84	C₃×#235	—	6	16	no	—
85	C₃²×Q₁₆	—	2	8	no	—
86	C₃²×Q₁₆	—	2	8	no	—
87	C₃²×Q₁₆	C₂×D₃	1	8	yes	—
88	C₃²×Q₁₆	C₂×D₃	1	8	yes	—
89	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
90	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
91	C₂×C₃²×C₈	—	2	4	no	—
92	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
93	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
94	#3756	C₂²×C₃	1	4	yes	—
95	#3755	C₂²×C₃	1	4	yes	—
96	#3748	C₂²×C₃	1	1	yes	characteristic
97	#3746	C₂²×C₃	1	1	yes	characteristic
98	#3745	C₂²×C₃	1	1	yes	characteristic
99	#3744	C₂²×C₃	1	2	yes	—
100	#3743	C₂²×C₃	1	2	yes	—
101	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	—
102	C₃×#216	—	3	16	no	—
103	C₃×#215	—	3	16	no	—
104	C₃×#208	—	3	4	no	—
105	C₃×Dic₁₂	—	3	4	no	—
106	C₃×D₂₄	—	3	4	no	—
107	C₃×#204	—	3	8	no	—
108	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
109	C₃×D₃×C₈	—	3	8	no	—
110	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₃⋊D₃	—	2	2	no	—
112	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
113	C₃³×C₄	—	2	4	no	—
114	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
115	C₃³×C₄	C₂⁴	1	1	yes	characteristic
116	C₃×C₃⋊Dic₃	—	2	2	no	—
117	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
118	C₃×2₋¹⁺⁴	—	9	2	no	—
119	#1007	—	3	8	no	—
120	C₃×#137	—	9	2	no	—
121	C₃×#137	—	9	4	no	—
122	C₃×#135	—	9	2	no	—
123	C₃×#135	—	9	1	no	—
124	C₂×C₃×Q₁₆	—	2	4	no	—
125	C₂×C₃×Q₁₆	—	9	2	no	—
126	C₂×C₃×Q₁₆	C₃×D₃	1	4	yes	complemented
127	C₂×C₃×Q₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
128	C₃×#131	—	9	1	no	—
129	#942	—	3	8	no	—
130	#919	—	3	8	no	—
131	#918	—	3	16	no	—
132	D₃×Q₁₆	—	3	8	no	—
133	#904	—	3	4	no	—
134	#901	—	3	4	no	—
135	C₃²×Q₈	—	2	2	no	—
136	C₃²×Q₈	—	2	16	no	—
137	C₃²×Q₈	—	2	8	no	—
138	C₃²×Q₈	—	4	8	no	—
139	C₃²×Q₈	C₂²×D₃	1	16	yes	—
140	C₃²×Q₈	C₂³×C₃	1	4	yes	—
141	C₂×C₃²×C₄	—	2	2	no	—
142	C₂×C₃²×C₄	—	2	4	no	—
143	C₂×C₃²×C₄	—	2	8	no	—
144	C₂×C₃²×C₄	—	4	8	no	—
145	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
146	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
147	#638	—	2	2	no	—
148	#638	C₃×D₄	1	2	yes	—
149	C₄⋊(C₃⋊D₃)	—	2	4	no	—
150	C₄⋊(C₃⋊D₃)	C₃×D₄	1	1	yes	characteristic
151	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
152	C₄×C₃⋊D₃	—	2	4	no	—
153	C₄×C₃⋊D₃	—	2	2	no	—
154	C₄×C₃⋊D₃	—	2	4	no	—
155	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
156	#634	—	2	4	no	—
157	#634	C₃×D₄	1	1	yes	characteristic
158	#634	C₂³×C₃	1	2	yes	—
159	C₃×#67	—	3	8	no	—
160	C₃×#67	—	6	8	no	—
161	C₃×D₁₂	—	3	4	no	—
162	C₃×D₁₂	—	3	8	no	—
163	C₃×D₁₂	—	6	16	no	—
164	C₃×C₄×D₃	—	3	8	no	—
165	C₃×C₄×D₃	—	6	16	no	—
166	C₃×C₄×D₃	—	6	16	no	—
167	C₃×C₄×D₃	—	6	8	no	—
168	C₃×Dic₆	—	3	4	no	—
169	C₃×Dic₆	—	3	8	no	—
170	C₃×Dic₆	—	6	16	no	—
171	C₃²×C₈	—	2	4	no	—
172	C₃²×C₈	—	2	4	no	—
173	C₃²×C₈	C₂²×D₃	1	4	yes	—
174	C₃²×C₈	C₂²×D₃	1	4	yes	—
175	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
176	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
177	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
178	C₃×C₃⋊C₈	—	3	8	no	—
179	#578	—	9	1	no	Sylow
180	C₂×C₃³	—	2	1	no	—
181	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
182	C₃×C₃⋊D₃	—	2	2	no	—
183	C₃×C₃⋊D₃	—	4	2	no	—
184	C₃×#41	—	9	1	no	—
185	C₃×#41	—	9	4	no	—
186	C₃×#41	—	9	2	no	—
187	C₃×#41	—	18	4	no	—
188	C₃×#41	—	18	2	no	—
189	C₂×C₃×Q₈	—	2	8	no	—
190	C₂×C₃×Q₈	—	9	4	no	—
191	C₂×C₃×Q₈	—	18	2	no	—
192	C₂×C₃×Q₈	C₂×C₃×D₃	1	8	yes	—
193	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	2	yes	—
194	#239	—	3	16	no	—
195	#239	—	6	8	no	—
196	D₃×Q₈	—	3	16	no	—
197	D₃×Q₈	—	6	8	no	—
198	#235	—	3	4	no	—
199	#235	—	3	8	no	—
200	#235	—	6	16	no	—
201	C₃×Q₁₆	—	2	8	no	—
202	C₃×Q₁₆	—	2	8	no	—
203	C₃×Q₁₆	—	9	4	no	—
204	C₃×Q₁₆	—	9	1	no	—
205	C₃×Q₁₆	C₂×C₃×D₃	1	8	yes	—
206	C₃×Q₁₆	C₂×C₃×D₃	1	8	yes	—
207	C₃×Q₁₆	C₂×C₃⋊D₃	1	2	yes	—
208	C₃×Q₁₆	C₂×C₃⋊D₃	1	2	yes	—
209	C₃×SD₁₆	—	9	4	no	—
210	C₃×SD₁₆	—	9	2	no	—
211	C₃×D₈	—	9	1	no	—
212	C₃×M₁₆	—	9	1	no	—
213	C₃×M₁₆	—	9	2	no	—
214	C₂×C₃×C₈	—	2	4	no	—
215	C₂×C₃×C₈	—	9	2	no	—
216	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
217	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
218	#216	—	3	16	no	—
219	#215	—	3	16	no	—
220	#208	—	3	4	no	—
221	Dic₁₂	—	3	4	no	—
222	D₂₄	—	3	4	no	—
223	#204	—	3	8	no	—
224	ΓL(1,𝔽₂₅)	—	3	8	no	—
225	D₃×C₈	—	3	8	no	—
226	C₂²×C₃²	—	2	4	no	—
227	C₂²×C₃²	D₃×D₄	1	4	yes	—
228	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₃⋊D₃	—	2	2	no	—
230	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
231	C₂×C₃×D₃	—	3	8	no	—
232	C₂×C₃×D₃	—	6	8	no	—
233	C₃²×C₄	—	2	4	no	—
234	C₃²×C₄	—	2	4	no	—
235	C₃²×C₄	—	2	4	no	—
236	C₃²×C₄	—	2	16	no	—
237	C₃²×C₄	—	4	16	no	—
238	C₃²×C₄	D₃×D₄	1	4	yes	—
239	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₃²×C₄	C₂³×D₃	1	4	yes	—
241	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
242	C₃⋊Dic₃	—	2	2	no	—
243	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
244	C₃×Dic₃	—	3	8	no	—
245	C₃×Dic₃	—	6	8	no	—
246	2₋¹⁺⁴	—	9	2	no	—
247	#137	—	9	2	no	—
248	#137	—	9	4	no	—
249	#135	—	9	2	no	—
250	#135	—	9	1	no	—
251	C₂×Q₁₆	—	9	2	no	—
252	C₂×Q₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
253	#131	—	9	1	no	—
254	C₃³	#578	1	1	yes	characteristic, complemented, Sylow
255	C₃×Q₈	—	2	8	no	—
256	C₃×Q₈	—	2	2	no	—
257	C₃×Q₈	—	2	16	no	—
258	C₃×Q₈	—	4	8	no	—
259	C₃×Q₈	—	9	1	no	—
260	C₃×Q₈	—	9	2	no	—
261	C₃×Q₈	—	18	4	no	—
262	C₃×Q₈	C₂²×C₃×D₃	1	16	yes	—
263	C₃×Q₈	C₂²×C₃⋊D₃	1	4	yes	—
264	C₃×D₄	—	9	2	no	—
265	C₃×D₄	—	9	2	no	—
266	C₃×D₄	—	9	1	no	—
267	C₃×D₄	—	18	4	no	—
268	C₃×D₄	—	18	2	no	—
269	C₂×C₃×C₄	—	2	8	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	4	8	no	—
273	C₂×C₃×C₄	—	9	2	no	—
274	C₂×C₃×C₄	—	18	4	no	—
275	C₂×C₃×C₄	—	18	4	no	—
276	C₂×C₃×C₄	—	18	2	no	—
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
279	#67	—	3	8	no	—
280	#67	—	6	8	no	—
281	D₁₂	—	3	8	no	—
282	D₁₂	—	3	4	no	—
283	D₁₂	—	6	16	no	—
284	C₄×D₃	—	3	8	no	—
285	C₄×D₃	—	6	16	no	—
286	C₄×D₃	—	6	16	no	—
287	C₄×D₃	—	6	8	no	—
288	Dic₆	—	3	4	no	—
289	Dic₆	—	3	8	no	—
290	Dic₆	—	6	16	no	—
291	C₃×C₈	—	2	4	no	—
292	C₃×C₈	—	2	4	no	—
293	C₃×C₈	—	9	2	no	—
294	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
295	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
296	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
297	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
298	C₃⋊C₈	—	3	8	no	—
299	C₂×C₃²	—	2	8	no	—
300	C₂×C₃²	—	2	1	no	—
301	C₂×C₃²	—	2	4	no	—
302	C₂×C₃²	—	2	4	no	—
303	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
304	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
305	C₃⋊D₃	—	2	2	no	—
306	C₃⋊D₃	—	4	2	no	—
307	C₃×D₃	—	6	8	no	—
308	C₃×D₃	—	12	8	no	—
309	#41	—	9	1	no	—
310	#41	—	9	4	no	—
311	#41	—	9	2	no	—
312	#41	—	18	4	no	—
313	#41	—	18	2	no	—
314	C₂×Q₈	—	9	4	no	—
315	C₂×Q₈	—	18	2	no	—
316	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
317	Q₁₆	—	9	4	no	—
318	Q₁₆	—	9	1	no	—
319	Q₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	—
320	Q₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	—
321	SD₁₆	—	9	4	no	—
322	SD₁₆	—	9	2	no	—
323	D₈	—	9	1	no	—
324	M₁₆	—	9	1	no	—
325	M₁₆	—	9	2	no	—
326	C₂×C₈	—	9	2	no	—
327	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	9	2	no	—
330	C₂²×C₃	—	18	2	no	—
331	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
332	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
333	C₂×D₃	—	3	8	no	—
334	C₂×D₃	—	6	8	no	—
335	C₃×C₄	—	2	16	no	—
336	C₃×C₄	—	2	4	no	—
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	4	16	no	—
340	C₃×C₄	—	9	2	no	—
341	C₃×C₄	—	18	2	no	—
342	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
343	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
344	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
345	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
346	Dic₃	—	3	8	no	—
347	Dic₃	—	6	8	no	—
348	C₃²	—	2	4	no	—
349	C₃²	#5766	1	4	yes	complemented
350	C₃²	C₃×#578	1	1	yes	characteristic, complemented
351	Q₈	—	2	2	no	—
352	Q₈	—	9	1	no	—
353	Q₈	—	9	2	no	—
354	Q₈	—	18	4	no	—
355	Q₈	C₂²×C₃×C₃⋊D₃	1	4	yes	—
356	D₄	—	9	2	no	—
357	D₄	—	9	2	no	—
358	D₄	—	9	1	no	—
359	D₄	—	18	4	no	—
360	D₄	—	18	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	9	2	no	—
363	C₂×C₄	—	18	4	no	—
364	C₂×C₄	—	18	4	no	—
365	C₂×C₄	—	18	2	no	—
366	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
367	C₈	—	9	2	no	—
368	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
369	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
370	C₂×C₃	—	2	8	no	—
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	—	18	2	no	—
375	C₂×C₃	—	36	2	no	—
376	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
377	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
378	D₃	—	6	8	no	—
379	D₃	—	12	8	no	—
380	C₂²	—	9	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	9	2	no	—
385	C₄	—	18	2	no	—
386	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
387	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
388	C₃	—	2	4	no	—
389	C₃	C₃×#5766	1	4	yes	complemented
390	C₃	#10596237	1	1	yes	characteristic, direct product factor
391	C₂	—	2	1	no	—
392	C₂	—	18	2	no	—
393	C₂	—	36	2	no	—
394	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×Q₁₆	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₂×C₃×Q₁₆	C₃⋊D₃
hypocenter	C₃²	C₃×#578
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#64364	C₂	semidirect
2. C₂×C₃³×Q₁₆	C₂	semidirect
3. C₃×#64151	C₂	semidirect
4. C₃×#64128	C₂	semidirect
5. C₃×#64127	C₂	semidirect
6. C₃×Q₁₆×C₃⋊D₃	C₂	semidirect
7. C₃×#64113	C₂	semidirect
8. C₃×#64110	C₂	semidirect
9. #10596237	C₃	direct (N × H)
30. #64364	C₂×C₃	semidirect
33. C₂×C₃²×Q₁₆	D₃	semidirect
34. C₂×C₃²×Q₁₆	C₂×C₃	semidirect
35. #64151	C₂×C₃	semidirect
36. #64128	C₂×C₃	semidirect
37. #64127	C₂×C₃	semidirect
38. Q₁₆×C₃⋊D₃	C₂×C₃	semidirect
39. #64113	C₂×C₃	semidirect
40. #64110	C₂×C₃	semidirect
126. C₂×C₃×Q₁₆	C₃×D₃	semidirect
127. C₂×C₃×Q₁₆	C₃⋊D₃	semidirect
252. C₂×Q₁₆	C₃×C₃⋊D₃	semidirect
254. C₃³	#578	semidirect
349. C₃²	#5766	semidirect
350. C₃²	C₃×#578	semidirect
389. C₃	C₃×#5766	semidirect
390. C₃	#10596237	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#64364	2
C₂×C₃³×Q₁₆	2
C₃×#64151	2
C₃×#64128	2
C₃×#64127	2
C₃×Q₁₆×C₃⋊D₃	2
C₃×#64113	2
C₃×#64110	2
#10596237	3
C₃×#5766	3

Subgroups — C3×#10596237 #13179517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596237 #13179517