Subgroups — C₄×#3697⋊C₃ #13152317

Order 1728.

984 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3697⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#611⋊C₃	C₂	1	4	yes	maximal, complemented
4	#63488⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
6	#63434⋊C₃	C₂	1	2	yes	maximal, complemented
7	C₄²×AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
8	C₄×3₋¹⁺²⋊Q₈	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×#235	—	3	1	no	maximal
10	C₄×#3697	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄×3₋¹⁺²	C₂²	1	2	yes	—
12	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
13	C₂×#611⋊C₃	C₂²	1	2	yes	—
14	#3697⋊C₃	C₄	1	8	yes	direct product factor
15	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
16	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	4	yes	—
17	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
18	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₄²×3₋¹⁺²	C₂²	1	2	yes	—
20	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
21	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
22	#3676⋊C₃	C₂²	1	2	yes	—
23	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	4	yes	—
24	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
25	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	4	yes	—
26	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
27	C₄×3₋¹⁺²⋊C₄	C₂²	1	4	yes	—
28	C₂×C₃×#235	—	3	1	no	—
29	C₂×C₃²×C₄²	D₃	1	1	yes	characteristic
30	C₃×C₄×#67	—	3	4	no	—
31	C₃×#926	—	3	1	no	—
32	C₃×C₄×D₁₂	—	3	2	no	—
33	C₃×#872	—	3	2	no	—
34	C₃×C₄²×D₃	—	3	2	no	—
35	C₃×C₄×Dic₆	—	3	2	no	—
36	C₂×#3697	C₂×C₃	1	1	yes	characteristic
37	C₂×C₄²×C₉	—	2	1	no	—
38	C₂×C₄²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
39	C₄×#611	C₂×C₃	1	4	yes	complemented
40	#63488	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×D₃₆	C₂×C₃	1	2	yes	complemented
42	#63434	C₂×C₃	1	2	yes	complemented
43	C₄²×D₉	C₂×C₃	1	2	yes	complemented
44	C₄×Dic₁₈	C₂×C₃	1	2	yes	complemented
45	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
46	C₂²×AGL(1,ℤ/9)	C₂³	1	2	yes	—
47	C₂×C₄×3₋¹⁺²	—	2	4	no	—
48	C₂×C₄×3₋¹⁺²	C₂×C₄	1	4	yes	complemented
49	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
50	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
51	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
52	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
53	#611⋊C₃	C₂×C₄	1	8	yes	complemented
54	C₂×3₋¹⁺²⋊C₄	C₂³	1	4	yes	—
55	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
56	C₄⋊AGL(1,ℤ/9)	C₂×C₄	1	4	yes	complemented
57	C₄×AGL(1,ℤ/9)	—	2	8	no	—
58	C₄×AGL(1,ℤ/9)	C₂×C₄	1	8	yes	complemented
59	3₋¹⁺²⋊Q₈	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×#41	—	9	1	no	—
61	C₄×#235	—	3	1	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
63	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃×#67	—	3	2	no	—
65	C₃×#235	—	3	8	no	—
66	C₂×C₃×D₁₂	—	3	1	no	—
67	C₂×C₃×C₄×D₃	—	3	2	no	—
68	C₂×C₃×C₄×D₃	—	3	4	no	—
69	C₂×C₃×Dic₆	—	3	1	no	—
70	C₃²×C₄²	C₂×D₃	1	2	yes	—
71	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
73	C₃×#217	—	3	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
75	C₃×C₄⋊Dic₃	—	3	2	no	—
76	C₃×Dic₃⋊C₄	—	3	4	no	—
77	C₃×C₄×Dic₃	—	3	2	no	—
78	C₃×C₄×Dic₃	—	3	4	no	—
79	C₂²×C₄×C₉	—	2	2	no	—
80	C₂²×C₄×C₉	—	2	1	no	—
81	C₂²×C₄×C₉	C₂²×C₃	1	2	yes	—
82	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
83	C₂×#611	C₂²×C₃	1	2	yes	—
84	#3697	C₃×C₄	1	8	yes	complemented
85	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
87	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
88	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
89	C₄²×C₉	—	2	2	no	—
90	C₄²×C₉	—	2	1	no	—
91	C₄²×C₉	—	2	1	no	—
92	C₄²×C₉	C₂²×C₃	1	2	yes	—
93	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
94	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
95	#3676	C₂²×C₃	1	2	yes	—
96	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
97	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
98	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
99	C₄×Dic₉	C₂²×C₃	1	2	yes	—
100	C₄×Dic₉	C₂²×C₃	1	4	yes	—
101	C₂²×3₋¹⁺²	—	2	2	no	—
102	C₂²×3₋¹⁺²	C₂²×C₄	1	2	yes	—
103	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
104	C₂×AGL(1,ℤ/9)	—	2	4	no	—
105	C₂×AGL(1,ℤ/9)	C₂²×C₄	1	4	yes	—
106	C₄×3₋¹⁺²	—	2	2	no	—
107	C₄×3₋¹⁺²	C₂²×C₄	1	2	yes	—
108	C₄×3₋¹⁺²	C₂²×C₄	1	2	yes	—
109	C₄×3₋¹⁺²	#41	1	4	yes	complemented
110	3₋¹⁺²⋊C₄	—	2	4	no	—
111	3₋¹⁺²⋊C₄	C₂²×C₄	1	4	yes	—
112	C₂×C₃×#41	—	9	1	no	—
113	C₂×#235	—	3	1	no	—
114	C₃×C₄×Q₈	—	9	2	no	—
115	C₃×C₄×D₄	—	9	2	no	—
116	C₃×C₄×D₄	—	9	4	no	—
117	C₃×#117	—	9	2	no	—
118	C₃×#117	—	9	1	no	—
119	C₂×C₃×C₄²	—	3	1	no	—
120	C₂×C₃×C₄²	—	9	2	no	—
121	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
122	C₄×#67	—	3	4	no	—
123	#926	—	3	1	no	—
124	C₄×D₁₂	—	3	2	no	—
125	#872	—	3	2	no	—
126	C₄²×D₃	—	3	2	no	—
127	C₄×Dic₆	—	3	2	no	—
128	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₃×D₃	—	3	2	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
132	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
133	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
136	C₃×#67	—	3	8	no	—
137	C₂×C₃×Dic₃	—	3	2	no	—
138	C₂×C₃×Dic₃	—	3	4	no	—
139	C₃×D₁₂	—	3	4	no	—
140	C₃×C₄×D₃	—	3	8	no	—
141	C₃×C₄×D₃	—	6	8	no	—
142	C₃×Dic₆	—	3	4	no	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
145	C₂²×D₉	C₂³×C₃	1	2	yes	—
146	C₂×C₄×C₉	—	2	8	no	—
147	C₂×C₄×C₉	—	2	4	no	—
148	C₂×C₄×C₉	—	2	4	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	C₂×C₃×C₄	1	4	yes	complemented
154	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
155	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
158	#611	C₂×C₃×C₄	1	8	yes	complemented
159	C₂×Dic₉	C₂³×C₃	1	4	yes	—
160	C₂×Dic₉	C₂³×C₃	1	2	yes	—
161	D₃₆	C₂×C₃×C₄	1	4	yes	complemented
162	C₄×D₉	—	2	8	no	—
163	C₄×D₉	C₂×C₃×C₄	1	8	yes	complemented
164	Dic₁₈	C₂×C₃×C₄	1	4	yes	complemented
165	C₄×#41	—	9	1	no	Sylow
166	C₂×3₋¹⁺²	—	2	2	no	—
167	C₂×3₋¹⁺²	C₂³×C₄	1	1	yes	characteristic
168	C₂×3₋¹⁺²	C₂×#41	1	2	yes	—
169	AGL(1,ℤ/9)	—	2	4	no	—
170	C₃×#41	—	9	8	no	—
171	C₂×C₃×Q₈	—	9	1	no	—
172	C₂×C₃×D₄	—	9	1	no	—
173	C₂×C₃×D₄	—	9	2	no	—
174	C₂²×C₃×C₄	—	3	1	no	—
175	C₂²×C₃×C₄	—	3	2	no	—
176	C₂²×C₃×C₄	—	9	2	no	—
177	C₂²×C₃×C₄	—	9	4	no	—
178	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
179	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
180	C₂×#67	—	3	2	no	—
181	#235	—	3	8	no	—
182	C₂×D₁₂	—	3	1	no	—
183	C₂×C₄×D₃	—	3	2	no	—
184	C₂×C₄×D₃	—	3	4	no	—
185	C₂×Dic₆	—	3	1	no	—
186	C₃×C₄⋊C₄	—	9	4	no	—
187	C₃×C₄⋊C₄	—	9	2	no	—
188	C₃×C₂²⋊C₄	—	9	4	no	—
189	C₃×C₂²⋊C₄	—	9	2	no	—
190	C₃×C₄²	—	3	1	no	—
191	C₃×C₄²	—	3	2	no	—
192	C₃×C₄²	—	3	1	no	—
193	C₃×C₄²	—	9	2	no	—
194	C₃×C₄²	—	9	4	no	—
195	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
196	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
197	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
198	#217	—	3	2	no	—
199	(C₂×D₃)⋊C₄	—	3	4	no	—
200	C₄⋊Dic₃	—	3	2	no	—
201	Dic₃⋊C₄	—	3	4	no	—
202	C₄×Dic₃	—	3	4	no	—
203	C₄×Dic₃	—	3	2	no	—
204	C₂²×C₃²	—	2	2	no	—
205	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
206	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
207	C₂×C₃×D₃	—	3	4	no	—
208	C₂×C₃×D₃	—	6	4	no	—
209	C₃²×C₄	—	2	2	no	—
210	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
211	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
212	C₃²×C₄	#235	1	4	yes	—
213	C₃×Dic₃	—	3	4	no	—
214	C₃×Dic₃	—	6	4	no	—
215	C₂²×C₉	—	2	4	no	—
216	C₂²×C₉	—	2	2	no	—
217	C₂²×C₉	—	2	1	no	—
218	C₂²×C₉	—	2	2	no	—
219	C₂²×C₉	C₂²×C₃×C₄	1	2	yes	—
220	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
221	C₂×D₉	—	2	4	no	—
222	C₂×D₉	C₂²×C₃×C₄	1	4	yes	—
223	C₄×C₉	—	2	4	no	—
224	C₄×C₉	—	2	2	no	—
225	C₄×C₉	—	2	2	no	—
226	C₄×C₉	—	2	2	no	—
227	C₄×C₉	—	2	4	no	—
228	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
229	C₄×C₉	C₂²×C₃×C₄	1	2	yes	—
230	C₄×C₉	C₃×#41	1	4	yes	complemented
231	Dic₉	—	2	4	no	—
232	Dic₉	C₂²×C₃×C₄	1	4	yes	—
233	C₂×#41	—	9	1	no	—
234	C₄×Q₈	—	9	2	no	—
235	C₄×D₄	—	9	4	no	—
236	C₄×D₄	—	9	2	no	—
237	#117	—	9	1	no	—
238	#117	—	9	2	no	—
239	C₂×C₄²	—	9	2	no	—
240	C₂×C₄²	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
241	3₋¹⁺²	C₄×#41	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₃	—	3	1	no	—
243	C₂³×C₃	—	9	2	no	—
244	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
245	C₂²×D₃	—	3	2	no	—
246	C₃×Q₈	—	9	4	no	—
247	C₃×D₄	—	9	4	no	—
248	C₃×D₄	—	9	8	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	3	4	no	—
251	C₂×C₃×C₄	—	3	1	no	—
252	C₂×C₃×C₄	—	3	2	no	—
253	C₂×C₃×C₄	—	3	1	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	6	4	no	—
256	C₂×C₃×C₄	—	9	8	no	—
257	C₂×C₃×C₄	—	9	2	no	—
258	C₂×C₃×C₄	—	9	4	no	—
259	C₂×C₃×C₄	—	18	8	no	—
260	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
261	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
265	#67	—	3	8	no	—
266	C₂×Dic₃	—	3	2	no	—
267	C₂×Dic₃	—	3	4	no	—
268	D₁₂	—	3	4	no	—
269	C₄×D₃	—	3	8	no	—
270	C₄×D₃	—	6	8	no	—
271	Dic₆	—	3	4	no	—
272	C₂×C₃²	—	2	2	no	—
273	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
274	C₂×C₃²	C₂×#235	1	2	yes	—
275	C₃×D₃	—	6	4	no	—
276	C₂×C₉	—	2	4	no	—
277	C₂×C₉	—	2	2	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	—	2	2	no	—
280	C₂×C₉	C₂³×C₃×C₄	1	1	yes	characteristic
281	C₂×C₉	C₂×C₃×#41	1	2	yes	—
282	D₉	—	2	4	no	—
283	#41	—	9	8	no	—
284	C₂×Q₈	—	9	1	no	—
285	C₂×D₄	—	9	2	no	—
286	C₂×D₄	—	9	1	no	—
287	C₂²×C₄	—	9	2	no	—
288	C₂²×C₄	—	9	4	no	—
289	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
290	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
291	C₄⋊C₄	—	9	4	no	—
292	C₄⋊C₄	—	9	2	no	—
293	C₂²⋊C₄	—	9	2	no	—
294	C₂²⋊C₄	—	9	4	no	—
295	C₄²	—	9	2	no	—
296	C₄²	—	9	4	no	—
297	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
298	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
299	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	3	1	no	—
302	C₂²×C₃	—	3	2	no	—
303	C₂²×C₃	—	6	2	no	—
304	C₂²×C₃	—	9	4	no	—
305	C₂²×C₃	—	18	4	no	—
306	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
307	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
308	C₂×D₃	—	3	4	no	—
309	C₂×D₃	—	6	4	no	—
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	3	2	no	—
312	C₃×C₄	—	3	2	no	—
313	C₃×C₄	—	3	4	no	—
314	C₃×C₄	—	6	2	no	—
315	C₃×C₄	—	9	4	no	—
316	C₃×C₄	—	18	4	no	—
317	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
318	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
319	C₃×C₄	C₃×#235	1	4	yes	—
320	Dic₃	—	3	4	no	—
321	Dic₃	—	6	4	no	—
322	C₃²	C₄×#235	1	1	yes	characteristic
323	C₉	—	2	1	no	—
324	C₉	C₃×C₄×#41	1	1	yes	characteristic, complemented
325	C₂³	—	9	2	no	—
326	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
327	Q₈	—	9	4	no	—
328	D₄	—	9	8	no	—
329	D₄	—	9	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	9	2	no	—
332	C₂×C₄	—	9	8	no	—
333	C₂×C₄	—	9	4	no	—
334	C₂×C₄	—	18	8	no	—
335	C₂×C₄	C₄×AGL(1,ℤ/9)	1	4	yes	complemented
336	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
337	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
338	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
339	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	3	1	no	—
342	C₂×C₃	—	3	2	no	—
343	C₂×C₃	—	6	2	no	—
344	C₂×C₃	—	18	4	no	—
345	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃×#235	1	2	yes	—
347	D₃	—	6	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	9	4	no	—
350	C₂²	—	18	4	no	—
351	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	2	yes	—
352	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	9	4	no	—
355	C₄	—	18	4	no	—
356	C₄	C₂×C₄×AGL(1,ℤ/9)	1	2	yes	—
357	C₄	C₂×C₄×AGL(1,ℤ/9)	1	2	yes	—
358	C₄	#3697⋊C₃	1	4	yes	direct product factor
359	C₃	—	3	1	no	—
360	C₃	C₃×C₄×#235	1	1	yes	characteristic
361	C₂	—	2	2	no	—
362	C₂	—	18	4	no	—
363	C₂	C₂²×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
364	C₂	C₂×#3697⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×AGL(1,ℤ/9)
commutator	C₂×C₉	C₂³×C₃×C₄
Frattini, socle	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₄²×3₋¹⁺²	C₂
prime radical	C₂×#3697⋊C₃	C₂
cosocle	C₂²×C₉	C₂⁴×C₃
hypercenter	C₂×C₄²	AGL(1,ℤ/9)
hypocenter	C₉	C₃×C₄×#41
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄²×3₋¹⁺²	C₂	semidirect
3. C₄×#611⋊C₃	C₂	semidirect
4. #63488⋊C₃	C₂	semidirect
5. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
6. #63434⋊C₃	C₂	semidirect
7. C₄²×AGL(1,ℤ/9)	C₂	semidirect
8. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
10. C₄×#3697	C₃	semidirect
14. #3697⋊C₃	C₄	direct (N × H)
38. C₂×C₄²×C₉	C₂×C₃	semidirect
39. C₄×#611	C₂×C₃	semidirect
40. #63488	C₂×C₃	semidirect
41. C₄×D₃₆	C₂×C₃	semidirect
42. #63434	C₂×C₃	semidirect
43. C₄²×D₉	C₂×C₃	semidirect
44. C₄×Dic₁₈	C₂×C₃	semidirect
48. C₂×C₄×3₋¹⁺²	C₂×C₄	semidirect
53. #611⋊C₃	C₂×C₄	semidirect
56. C₄⋊AGL(1,ℤ/9)	C₂×C₄	semidirect
58. C₄×AGL(1,ℤ/9)	C₂×C₄	semidirect
59. 3₋¹⁺²⋊Q₈	C₂×C₄	semidirect
84. #3697	C₃×C₄	semidirect
109. C₄×3₋¹⁺²	#41	semidirect
153. C₂×C₄×C₉	C₂×C₃×C₄	semidirect
158. #611	C₂×C₃×C₄	semidirect
161. D₃₆	C₂×C₃×C₄	semidirect
163. C₄×D₉	C₂×C₃×C₄	semidirect
164. Dic₁₈	C₂×C₃×C₄	semidirect
230. C₄×C₉	C₃×#41	semidirect
240. C₂×C₄²	AGL(1,ℤ/9)	semidirect
241. 3₋¹⁺²	C₄×#41	semidirect
324. C₉	C₃×C₄×#41	semidirect
335. C₂×C₄	C₄×AGL(1,ℤ/9)	semidirect
358. C₄	#3697⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#3697⋊C₃	2
C₂×C₄²×3₋¹⁺²	2
C₄×#611⋊C₃	2
#63488⋊C₃	2
C₄×C₄⋊AGL(1,ℤ/9)	2
#63434⋊C₃	2
C₄²×AGL(1,ℤ/9)	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×C₄×#235	3
C₄×#3697	3

Subgroups — C4×#3697⋊C3 #13152317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#3697⋊C₃ #13152317