Subgroups — C₃×#10596221 #13179501

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃³×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64157	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64116	C₂	1	3	yes	maximal, complemented
5	C₃×M₁₆×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
6	C₃×#64110	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#3743	C₂	1	3	yes	maximal, complemented
8	#10596221	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#5750	—	3	4	no	maximal
10	C₃³×#41	C₂²	1	1	yes	characteristic
11	C₃×#3832	C₄	1	1	yes	characteristic
12	C₃×Q₈×C₃⋊D₃	C₄	1	1	yes	characteristic
13	C₃×#3830	C₄	1	3	yes	—
14	C₃×D₄×C₃⋊D₃	C₄	1	3	yes	—
15	C₃×#3828	C₂²	1	3	yes	—
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	3	yes	—
17	C₃³×M₁₆	C₂²	1	3	yes	complemented
18	C₂×C₃³×C₈	C₂²	1	3	yes	complemented
19	C₃×#3748	C₂²	1	3	yes	complemented
20	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	3	yes	complemented
21	C₃×#3743	C₂²	1	1	yes	characteristic
22	C₃×#3743	C₂²	1	3	yes	—
23	C₃×#3743	C₂²	1	3	yes	complemented
24	C₃×#3743	C₂²	1	3	yes	complemented
25	C₃×C₈×C₃⋊D₃	C₂²	1	6	yes	complemented
26	#41×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
27	C₃×D₃×#41	—	3	4	no	—
28	C₃²×#131	—	2	4	no	—
29	C₃²×#131	D₃	1	4	yes	complemented
30	C₃²×#131	C₂×C₃	1	1	yes	characteristic, complemented
31	#64157	C₂×C₃	1	1	yes	characteristic, complemented
32	#64116	C₂×C₃	1	3	yes	complemented
33	M₁₆×C₃⋊D₃	C₂×C₃	1	3	yes	complemented
34	#64110	C₂×C₃	1	3	yes	complemented
35	C₂×#3743	C₂×C₃	1	3	yes	complemented
36	C₃×#948	—	3	4	no	—
37	C₃×#907	—	3	12	no	—
38	C₃×D₃×M₁₆	—	3	12	no	—
39	C₃×#901	—	3	12	no	—
40	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	12	no	—
41	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	3	yes	—
42	C₃³×Q₈	C₂×C₄	1	1	yes	characteristic
43	C₃³×D₄	C₂×C₄	1	3	yes	—
44	C₂×C₃³×C₄	C₂³	1	3	yes	—
45	C₃×#638	C₂×C₄	1	6	yes	—
46	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
47	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	3	yes	—
48	C₃×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
49	C₃×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
50	C₃×C₄×C₃⋊D₃	C₂³	1	3	yes	—
51	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
52	C₃×#634	C₂×C₄	1	3	yes	—
53	C₃³×C₈	C₂³	1	3	yes	—
54	C₃³×C₈	C₂³	1	1	yes	characteristic
55	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	3	yes	—
56	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
57	C₃×#568	—	9	1	no	—
58	#5750	—	3	4	no	—
59	C₃²×#41	—	2	4	no	—
60	C₃²×#41	C₂×D₃	1	4	yes	—
61	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
62	#3832	C₃×C₄	1	1	yes	characteristic
63	Q₈×C₃⋊D₃	C₃×C₄	1	1	yes	characteristic
64	#3830	C₃×C₄	1	3	yes	—
65	D₄×C₃⋊D₃	C₃×C₄	1	3	yes	—
66	#3828	C₂²×C₃	1	3	yes	—
67	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	3	yes	—
68	C₃×#239	—	3	4	no	—
69	C₃×D₃×Q₈	—	3	4	no	—
70	C₃×#237	—	3	12	no	—
71	C₃×D₃×D₄	—	3	12	no	—
72	C₃×#235	—	3	12	no	—
73	C₂×C₃×C₄×D₃	—	3	12	no	—
74	C₃²×M₁₆	—	2	12	no	—
75	C₃²×M₁₆	C₂×D₃	1	12	yes	complemented
76	C₃²×M₁₆	C₂²×C₃	1	3	yes	complemented
77	C₂×C₃²×C₈	—	2	12	no	—
78	C₂×C₃²×C₈	C₂×D₃	1	12	yes	complemented
79	C₂×C₃²×C₈	C₂²×C₃	1	3	yes	complemented
80	#3748	C₂²×C₃	1	3	yes	complemented
81	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	3	yes	complemented
82	#3743	C₂²×C₃	1	1	yes	characteristic
83	#3743	C₂²×C₃	1	3	yes	—
84	#3743	C₂²×C₃	1	3	yes	complemented
85	#3743	C₂²×C₃	1	3	yes	complemented
86	C₈×C₃⋊D₃	C₂²×C₃	1	6	yes	complemented
87	C₃×#208	—	3	12	no	—
88	C₂×C₃×C₃⋊C₈	—	3	12	no	—
89	C₃×ΓL(1,𝔽₂₅)	—	3	4	no	—
90	C₃×ΓL(1,𝔽₂₅)	—	3	12	no	—
91	C₃×ΓL(1,𝔽₂₅)	—	3	12	no	—
92	C₃×ΓL(1,𝔽₂₅)	—	3	12	no	—
93	C₃×D₃×C₈	—	3	24	no	—
94	C₂²×C₃³	C₂²×C₄	1	3	yes	—
95	C₂×C₃×C₃⋊D₃	—	4	3	no	—
96	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	3	yes	—
98	C₃³×C₄	C₂²×C₄	1	3	yes	—
99	C₃³×C₄	C₂⁴	1	1	yes	characteristic
100	C₃×C₃⋊Dic₃	C₂²×C₄	1	3	yes	—
101	C₃×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×#41	—	9	1	no	—
103	D₃×#41	—	3	4	no	—
104	C₃×#131	—	2	4	no	—
105	C₃×#131	—	9	1	no	—
106	C₃×#131	—	9	3	no	—
107	C₃×#131	—	9	3	no	—
108	C₃×#131	C₃×D₃	1	4	yes	complemented
109	C₃×#131	C₃⋊D₃	1	1	yes	characteristic, complemented
110	C₂×C₃×M₁₆	—	9	3	no	—
111	C₂×C₃×M₁₆	—	9	3	no	—
112	#948	—	3	4	no	—
113	#907	—	3	12	no	—
114	D₃×M₁₆	—	3	12	no	—
115	#901	—	3	12	no	—
116	C₂×ΓL(1,𝔽₂₅)	—	3	12	no	—
117	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	3	yes	—
118	C₂²×C₃×D₃	—	3	12	no	—
119	C₃²×Q₈	—	2	4	no	—
120	C₃²×Q₈	C₄×D₃	1	4	yes	—
121	C₃²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
122	C₃²×D₄	—	2	12	no	—
123	C₃²×D₄	C₄×D₃	1	12	yes	—
124	C₃²×D₄	C₂×C₃×C₄	1	3	yes	—
125	C₂×C₃²×C₄	—	2	12	no	—
126	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	3	yes	—
128	#638	C₂×C₃×C₄	1	6	yes	—
129	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	3	yes	—
130	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	3	yes	—
131	C₄×C₃⋊D₃	C₂×C₃×C₄	1	3	yes	—
132	C₄×C₃⋊D₃	C₂×C₃×C₄	1	3	yes	—
133	C₄×C₃⋊D₃	C₂³×C₃	1	3	yes	—
134	C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
135	#634	C₂×C₃×C₄	1	3	yes	—
136	C₃×#67	—	3	24	no	—
137	C₂×C₃×Dic₃	—	3	12	no	—
138	C₃×D₁₂	—	3	12	no	—
139	C₃×C₄×D₃	—	3	12	no	—
140	C₃×C₄×D₃	—	3	12	no	—
141	C₃×C₄×D₃	—	3	12	no	—
142	C₃×C₄×D₃	—	3	4	no	—
143	C₃×Dic₆	—	3	12	no	—
144	C₃²×C₈	—	2	4	no	—
145	C₃²×C₈	—	2	12	no	—
146	C₃²×C₈	C₂²×D₃	1	12	yes	—
147	C₃²×C₈	C₂²×D₃	1	4	yes	—
148	C₃²×C₈	C₂³×C₃	1	3	yes	—
149	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
150	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	3	yes	—
151	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
152	C₃×C₃⋊C₈	—	3	12	no	—
153	C₃×C₃⋊C₈	—	3	4	no	—
154	#568	—	9	1	no	Sylow
155	C₂×C₃³	—	2	3	no	—
156	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
157	C₃×C₃⋊D₃	—	2	1	no	—
158	C₃×C₃⋊D₃	—	2	3	no	—
159	C₃×#41	—	2	4	no	—
160	C₃×#41	—	9	1	no	—
161	C₃×#41	—	9	3	no	—
162	C₃×#41	—	9	3	no	—
163	C₃×#41	C₂×C₃×D₃	1	4	yes	—
164	C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic
165	C₂×C₃×Q₈	—	9	1	no	—
166	C₂×C₃×D₄	—	9	3	no	—
167	C₂²×C₃×C₄	—	9	3	no	—
168	#239	—	3	4	no	—
169	D₃×Q₈	—	3	4	no	—
170	#237	—	3	12	no	—
171	D₃×D₄	—	3	12	no	—
172	#235	—	3	12	no	—
173	C₂×C₄×D₃	—	3	12	no	—
174	C₃×M₁₆	—	2	12	no	—
175	C₃×M₁₆	—	9	3	no	—
176	C₃×M₁₆	—	9	3	no	—
177	C₃×M₁₆	—	9	1	no	—
178	C₃×M₁₆	—	9	3	no	—
179	C₃×M₁₆	—	9	3	no	—
180	C₃×M₁₆	C₂×C₃×D₃	1	12	yes	complemented
181	C₃×M₁₆	C₂×C₃⋊D₃	1	3	yes	complemented
182	C₂×C₃×C₈	—	2	12	no	—
183	C₂×C₃×C₈	—	9	3	no	—
184	C₂×C₃×C₈	—	9	6	no	—
185	C₂×C₃×C₈	C₂×C₃×D₃	1	12	yes	complemented
186	C₂×C₃×C₈	C₂×C₃⋊D₃	1	3	yes	complemented
187	#208	—	3	12	no	—
188	C₂×C₃⋊C₈	—	3	12	no	—
189	ΓL(1,𝔽₂₅)	—	3	4	no	—
190	ΓL(1,𝔽₂₅)	—	3	12	no	—
191	ΓL(1,𝔽₂₅)	—	3	12	no	—
192	ΓL(1,𝔽₂₅)	—	3	12	no	—
193	D₃×C₈	—	3	24	no	—
194	C₂²×C₃²	—	2	12	no	—
195	C₂²×C₃²	C₂×C₄×D₃	1	12	yes	—
196	C₂²×C₃²	C₂²×C₃×C₄	1	3	yes	—
197	C₂×C₃⋊D₃	—	4	3	no	—
198	C₂×C₃⋊D₃	C₂²×C₃×C₄	1	1	yes	characteristic
199	C₂×C₃⋊D₃	C₂²×C₃×C₄	1	3	yes	—
200	C₂×C₃×D₃	—	3	4	no	—
201	C₂×C₃×D₃	—	3	12	no	—
202	C₂×C₃×D₃	—	12	12	no	—
203	C₃²×C₄	—	2	4	no	—
204	C₃²×C₄	—	2	12	no	—
205	C₃²×C₄	C₂×C₄×D₃	1	12	yes	—
206	C₃²×C₄	C₂²×C₃×C₄	1	3	yes	—
207	C₃²×C₄	C₂³×D₃	1	4	yes	—
208	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
209	C₃⋊Dic₃	C₂²×C₃×C₄	1	3	yes	—
210	C₃⋊Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₃×Dic₃	—	3	12	no	—
212	C₃×Dic₃	—	3	4	no	—
213	C₂×#41	—	9	1	no	—
214	#131	—	9	1	no	—
215	#131	—	9	3	no	—
216	#131	—	9	3	no	—
217	#131	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
218	C₂×M₁₆	—	9	3	no	—
219	C₂×M₁₆	—	9	3	no	—
220	C₃³	#568	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₃	—	9	3	no	—
222	C₂²×D₃	—	3	12	no	—
223	C₃×Q₈	—	2	4	no	—
224	C₃×Q₈	—	9	3	no	—
225	C₃×Q₈	C₃×C₄×D₃	1	4	yes	—
226	C₃×Q₈	C₄×C₃⋊D₃	1	1	yes	characteristic
227	C₃×D₄	—	2	12	no	—
228	C₃×D₄	—	9	6	no	—
229	C₃×D₄	—	9	3	no	—
230	C₃×D₄	C₃×C₄×D₃	1	12	yes	—
231	C₃×D₄	C₄×C₃⋊D₃	1	3	yes	—
232	C₂×C₃×C₄	—	2	12	no	—
233	C₂×C₃×C₄	—	9	3	no	—
234	C₂×C₃×C₄	—	9	3	no	—
235	C₂×C₃×C₄	—	9	1	no	—
236	C₂×C₃×C₄	—	9	3	no	—
237	C₂×C₃×C₄	—	9	3	no	—
238	C₂×C₃×C₄	C₂²×C₃×D₃	1	12	yes	—
239	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	3	yes	—
240	#67	—	3	24	no	—
241	C₂×Dic₃	—	3	12	no	—
242	D₁₂	—	3	12	no	—
243	C₄×D₃	—	3	12	no	—
244	C₄×D₃	—	3	4	no	—
245	C₄×D₃	—	3	12	no	—
246	C₄×D₃	—	3	12	no	—
247	Dic₆	—	3	12	no	—
248	C₃×C₈	—	2	4	no	—
249	C₃×C₈	—	2	12	no	—
250	C₃×C₈	—	9	3	no	—
251	C₃×C₈	—	9	1	no	—
252	C₃×C₈	C₂²×C₃×D₃	1	12	yes	—
253	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
254	C₃×C₈	C₂²×C₃⋊D₃	1	3	yes	—
255	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
256	C₃⋊C₈	—	3	12	no	—
257	C₃⋊C₈	—	3	4	no	—
258	C₂×C₃²	—	2	3	no	—
259	C₂×C₃²	—	2	4	no	—
260	C₂×C₃²	—	2	12	no	—
261	C₂×C₃²	—	4	12	no	—
262	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
263	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
264	C₃⋊D₃	—	2	1	no	—
265	C₃⋊D₃	—	2	3	no	—
266	C₃×D₃	—	6	12	no	—
267	C₃×D₃	—	6	4	no	—
268	#41	—	9	1	no	—
269	#41	—	9	3	no	—
270	#41	—	9	3	no	—
271	#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
272	C₂×Q₈	—	9	1	no	—
273	C₂×D₄	—	9	3	no	—
274	C₂²×C₄	—	9	3	no	—
275	M₁₆	—	9	3	no	—
276	M₁₆	—	9	3	no	—
277	M₁₆	—	9	1	no	—
278	M₁₆	—	9	3	no	—
279	M₁₆	—	9	3	no	—
280	M₁₆	C₂×C₃×C₃⋊D₃	1	3	yes	complemented
281	C₂×C₈	—	9	3	no	—
282	C₂×C₈	—	9	6	no	—
283	C₂×C₈	C₂×C₃×C₃⋊D₃	1	3	yes	complemented
284	C₂²×C₃	—	2	12	no	—
285	C₂²×C₃	—	9	1	no	—
286	C₂²×C₃	—	9	3	no	—
287	C₂²×C₃	—	36	3	no	—
288	C₂²×C₃	C₂×C₃×C₄×D₃	1	12	yes	—
289	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	3	yes	—
290	C₂×D₃	—	3	4	no	—
291	C₂×D₃	—	3	12	no	—
292	C₂×D₃	—	12	12	no	—
293	C₃×C₄	—	2	4	no	—
294	C₃×C₄	—	2	12	no	—
295	C₃×C₄	—	9	1	no	—
296	C₃×C₄	—	9	3	no	—
297	C₃×C₄	C₂×C₃×C₄×D₃	1	12	yes	—
298	C₃×C₄	C₂×C₄×C₃⋊D₃	1	3	yes	—
299	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
300	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
301	Dic₃	—	3	12	no	—
302	Dic₃	—	3	4	no	—
303	C₃²	—	2	4	no	—
304	C₃²	#5750	1	4	yes	complemented
305	C₃²	C₃×#568	1	1	yes	characteristic, complemented
306	C₂³	—	9	3	no	—
307	Q₈	—	9	3	no	—
308	Q₈	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
309	D₄	—	9	6	no	—
310	D₄	—	9	3	no	—
311	D₄	C₃×C₄×C₃⋊D₃	1	3	yes	—
312	C₂×C₄	—	9	3	no	—
313	C₂×C₄	—	9	3	no	—
314	C₂×C₄	—	9	1	no	—
315	C₂×C₄	—	9	3	no	—
316	C₂×C₄	—	9	3	no	—
317	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	3	yes	—
318	C₈	—	9	1	no	—
319	C₈	—	9	3	no	—
320	C₈	C₂²×C₃×C₃⋊D₃	1	3	yes	—
321	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
322	C₂×C₃	—	2	12	no	—
323	C₂×C₃	—	2	3	no	—
324	C₂×C₃	—	2	4	no	—
325	C₂×C₃	—	4	12	no	—
326	C₂×C₃	—	18	1	no	—
327	C₂×C₃	—	18	3	no	—
328	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
329	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
330	D₃	—	6	4	no	—
331	D₃	—	6	12	no	—
332	C₂²	—	9	1	no	—
333	C₂²	—	9	3	no	—
334	C₂²	—	36	3	no	—
335	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	3	yes	—
336	C₄	—	9	1	no	—
337	C₄	—	9	3	no	—
338	C₄	C₂×C₃×C₄×C₃⋊D₃	1	3	yes	—
339	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
340	C₃	—	2	4	no	—
341	C₃	C₃×#5750	1	4	yes	complemented
342	C₃	#10596221	1	1	yes	characteristic, direct product factor
343	C₂	—	2	3	no	—
344	C₂	—	18	1	no	—
345	C₂	—	18	3	no	—
346	C₂	C₂²×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂³×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#131	C₂
socle	C₂×C₃³	C₂³×C₄
prime radical	C₃×#41×C₃⋊D₃	C₂
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₃×#131	C₃⋊D₃
hypocenter	C₃²	C₃×#568
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₃×#131

Complements

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

N	H ≅ G/N	type
2. C₃³×#131	C₂	semidirect
3. C₃×#64157	C₂	semidirect
4. C₃×#64116	C₂	semidirect
5. C₃×M₁₆×C₃⋊D₃	C₂	semidirect
6. C₃×#64110	C₂	semidirect
7. C₂×C₃×#3743	C₂	semidirect
8. #10596221	C₃	direct (N × H)
17. C₃³×M₁₆	C₂²	semidirect
18. C₂×C₃³×C₈	C₂²	semidirect
19. C₃×#3748	C₂²	semidirect
20. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
23. C₃×#3743	C₂²	semidirect
24. C₃×#3743	C₂²	semidirect
25. C₃×C₈×C₃⋊D₃	C₂²	semidirect
29. C₃²×#131	D₃	semidirect
30. C₃²×#131	C₂×C₃	semidirect
31. #64157	C₂×C₃	semidirect
32. #64116	C₂×C₃	semidirect
33. M₁₆×C₃⋊D₃	C₂×C₃	semidirect
34. #64110	C₂×C₃	semidirect
35. C₂×#3743	C₂×C₃	semidirect
75. C₃²×M₁₆	C₂×D₃	semidirect
76. C₃²×M₁₆	C₂²×C₃	semidirect
78. C₂×C₃²×C₈	C₂×D₃	semidirect
79. C₂×C₃²×C₈	C₂²×C₃	semidirect
80. #3748	C₂²×C₃	semidirect
81. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
84. #3743	C₂²×C₃	semidirect
85. #3743	C₂²×C₃	semidirect
86. C₈×C₃⋊D₃	C₂²×C₃	semidirect
108. C₃×#131	C₃×D₃	semidirect
109. C₃×#131	C₃⋊D₃	semidirect
180. C₃×M₁₆	C₂×C₃×D₃	semidirect
181. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
185. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
186. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
217. #131	C₃×C₃⋊D₃	semidirect
220. C₃³	#568	semidirect
280. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
283. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
304. C₃²	#5750	semidirect
305. C₃²	C₃×#568	semidirect
341. C₃	C₃×#5750	semidirect
342. C₃	#10596221	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×#41×C₃⋊D₃	2
C₃³×#131	2
C₃×#64157	2
C₃×#64116	2
C₃×M₁₆×C₃⋊D₃	2
C₃×#64110	2
C₂×C₃×#3743	2
#10596221	3
C₃×#5750	3

Subgroups — C3×#10596221 #13179501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596221 #13179501