Subgroups — C₂×C₆₇×#1698 #30698402

Order 17152.

702 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#477×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#446×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1698	C₂	1	8	yes	maximal, direct product factor
6	C₂×#335×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#333×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#331×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×SD₁₆×C₆₇	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	#486×C₆₇	—	2	2	no	—
14	#486×C₆₇	C₂²	1	4	yes	—
15	#477×C₆₇	—	2	2	no	—
16	#477×C₆₇	C₂²	1	4	yes	complemented
17	#460×C₆₇	—	2	2	no	—
18	#460×C₆₇	C₂²	1	4	yes	—
19	#446×C₆₇	—	2	2	no	—
20	#446×C₆₇	C₂²	1	4	yes	complemented
21	C₂×#107×C₆₇	—	2	1	no	—
22	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
23	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₇	—	2	1	no	—
27	C₂×#102×C₆₇	—	2	1	no	—
28	C₂×#102×C₆₇	—	2	1	no	—
29	C₂×#102×C₆₇	—	2	1	no	—
30	C₂×#97×C₆₇	—	2	1	no	—
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#335×C₆₇	C₂²	1	4	yes	complemented
33	#333×C₆₇	C₂²	1	4	yes	complemented
34	#331×C₆₇	C₂²	1	4	yes	—
35	C₂²×Q₈×C₆₇	—	2	1	no	—
36	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₆₇	—	2	1	no	—
38	C₂²×D₄×C₆₇	—	2	1	no	—
39	C₂²×D₄×C₆₇	—	2	1	no	—
40	C₂×SD₁₆×C₆₇	—	2	4	no	—
41	C₂×SD₁₆×C₆₇	—	4	4	no	—
42	C₂²×C₈×C₆₇	—	2	1	no	—
43	C₂²×C₈×C₆₇	—	2	1	no	—
44	C₂²×C₈×C₆₇	—	2	1	no	—
45	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₆₇	—	2	1	no	—
48	C₄⋊Q₈×C₆₇	—	2	1	no	—
49	C₄⋊Q₈×C₆₇	—	2	1	no	—
50	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
51	#127×C₆₇	—	2	1	no	—
52	#127×C₆₇	—	2	1	no	—
53	#127×C₆₇	—	2	1	no	—
54	#127×C₆₇	C₂³	1	2	yes	—
55	C₄×Q₈×C₆₇	—	2	1	no	—
56	C₄×Q₈×C₆₇	—	2	1	no	—
57	C₄×Q₈×C₆₇	D₄	1	2	yes	—
58	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	—	2	1	no	—
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	#107×C₆₇	—	2	4	no	—
66	C₄⋊C₈×C₆₇	—	2	4	no	—
67	C₄⋊C₈×C₆₇	—	2	1	no	—
68	C₄⋊C₈×C₆₇	—	2	1	no	—
69	C₄⋊C₈×C₆₇	—	2	1	no	—
70	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
71	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
73	#103×C₆₇	—	2	4	no	—
74	#102×C₆₇	—	2	4	no	—
75	#102×C₆₇	—	2	4	no	—
76	#102×C₆₇	—	2	4	no	—
77	#97×C₆₇	—	2	4	no	—
78	C₄×C₈×C₆₇	D₄	1	2	yes	—
79	C₄×C₈×C₆₇	C₂³	1	2	yes	—
80	C₂⁴×C₆₇	—	4	1	no	—
81	C₂×Q₈×C₆₇	—	2	1	no	—
82	C₂×Q₈×C₆₇	—	2	2	no	—
83	C₂×Q₈×C₆₇	—	2	2	no	—
84	C₂×Q₈×C₆₇	—	2	2	no	—
85	C₂×Q₈×C₆₇	—	4	1	no	—
86	C₂×Q₈×C₆₇	—	8	2	no	—
87	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	2	no	—
90	C₂×D₄×C₆₇	—	2	2	no	—
91	C₂×D₄×C₆₇	—	4	1	no	—
92	C₂×D₄×C₆₇	—	4	1	no	—
93	C₂×D₄×C₆₇	—	4	1	no	—
94	C₂×D₄×C₆₇	—	4	2	no	—
95	C₂×D₄×C₆₇	—	4	2	no	—
96	C₂×D₄×C₆₇	—	4	2	no	—
97	C₂×D₄×C₆₇	—	4	2	no	—
98	C₂×D₄×C₆₇	—	8	2	no	—
99	C₂²×C₄×C₆₇	—	2	1	no	—
100	C₂²×C₄×C₆₇	—	2	1	no	—
101	C₂²×C₄×C₆₇	—	4	1	no	—
102	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
105	SD₁₆×C₆₇	—	4	8	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	—	2	2	no	—
108	C₂×C₈×C₆₇	—	2	2	no	—
109	C₂×C₈×C₆₇	—	2	2	no	—
110	C₂×C₈×C₆₇	—	2	2	no	—
111	C₂×C₈×C₆₇	—	4	2	no	—
112	C₂×C₈×C₆₇	—	4	2	no	—
113	C₂×C₈×C₆₇	—	4	2	no	—
114	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₆₇	—	2	2	no	—
117	C₄⋊C₄×C₆₇	—	2	1	no	—
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	4	1	no	—
122	C₄⋊C₄×C₆₇	—	4	1	no	—
123	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
124	C₄²×C₆₇	—	2	2	no	—
125	C₄²×C₆₇	—	2	2	no	—
126	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₆₇	#41	1	1	yes	characteristic
129	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
130	C₂³×C₆₇	—	4	2	no	—
131	C₂³×C₆₇	—	8	2	no	—
132	C₂³×C₆₇	—	8	2	no	—
133	C₂³×C₆₇	—	8	2	no	—
134	C₂³×C₆₇	#121	1	1	yes	characteristic
135	Q₈×C₆₇	—	2	2	no	—
136	Q₈×C₆₇	—	2	2	no	—
137	Q₈×C₆₇	—	4	2	no	—
138	Q₈×C₆₇	—	8	2	no	—
139	Q₈×C₆₇	—	8	2	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	4	2	no	—
144	D₄×C₆₇	—	8	2	no	—
145	D₄×C₆₇	—	8	2	no	—
146	D₄×C₆₇	—	8	2	no	—
147	D₄×C₆₇	—	8	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	8	2	no	—
155	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#135	1	2	yes	—
159	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₆₇	#137	1	2	yes	—
161	C₂×C₄×C₆₇	#137	1	2	yes	—
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
165	C₈×C₆₇	—	2	2	no	—
166	C₈×C₆₇	—	2	2	no	—
167	C₈×C₆₇	—	4	2	no	—
168	C₈×C₆₇	—	4	2	no	—
169	C₈×C₆₇	—	4	2	no	—
170	C₂²×C₆₇	—	8	2	no	—
171	C₂²×C₆₇	—	8	2	no	—
172	C₂²×C₆₇	—	8	2	no	—
173	C₂²×C₆₇	—	16	4	no	—
174	C₂²×C₆₇	#464	1	2	yes	—
175	C₂²×C₆₇	#468	1	2	yes	—
176	C₂²×C₆₇	#472	1	2	yes	—
177	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	4	2	no	—
181	C₄×C₆₇	—	4	2	no	—
182	C₄×C₆₇	—	8	2	no	—
183	C₄×C₆₇	#464	1	2	yes	—
184	C₄×C₆₇	#468	1	2	yes	—
185	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
186	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
188	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
189	C₂×#1698	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₆₇	—	16	2	no	—
191	C₂×C₆₇	#1698	1	4	yes	direct product factor
192	C₂×C₆₇	C₂×#464	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#468	1	1	yes	characteristic
194	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
195	C₂×#486	C₂×C₆₇	1	1	yes	characteristic
196	C₂×#477	C₂×C₆₇	1	1	yes	characteristic, complemented
197	C₂×#460	C₂×C₆₇	1	1	yes	characteristic
198	C₂×#446	C₂×C₆₇	1	1	yes	characteristic, complemented
199	#1698	C₂×C₆₇	1	8	yes	direct product factor
200	C₂×#335	C₂×C₆₇	1	1	yes	characteristic, complemented
201	C₂×#333	C₂×C₆₇	1	1	yes	characteristic, complemented
202	C₂×#331	C₂×C₆₇	1	1	yes	characteristic
203	C₆₇	C₂×#1698	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
206	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
208	#486	—	2	2	no	—
209	#486	C₂²×C₆₇	1	4	yes	—
210	#477	—	2	2	no	—
211	#477	C₂²×C₆₇	1	4	yes	complemented
212	#460	—	2	2	no	—
213	#460	C₂²×C₆₇	1	4	yes	—
214	#446	—	2	2	no	—
215	#446	C₂²×C₆₇	1	4	yes	complemented
216	C₂×#107	—	2	1	no	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
221	C₂×#103	—	2	1	no	—
222	C₂×#102	—	2	1	no	—
223	C₂×#102	—	2	1	no	—
224	C₂×#102	—	2	1	no	—
225	C₂×#97	—	2	1	no	—
226	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
227	#335	C₂²×C₆₇	1	4	yes	complemented
228	#333	C₂²×C₆₇	1	4	yes	complemented
229	#331	C₂²×C₆₇	1	4	yes	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	4	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	—	2	1	no	—
249	#127	C₂³×C₆₇	1	2	yes	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	D₄×C₆₇	1	2	yes	—
253	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
260	#107	—	2	4	no	—
261	C₄⋊C₈	—	2	4	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
266	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
267	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
268	#103	—	2	4	no	—
269	#102	—	2	4	no	—
270	#102	—	2	4	no	—
271	#102	—	2	4	no	—
272	#97	—	2	4	no	—
273	C₄×C₈	D₄×C₆₇	1	2	yes	—
274	C₄×C₈	C₂³×C₆₇	1	2	yes	—
275	C₂⁴	—	4	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	8	2	no	—
282	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
299	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
310	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
323	C₄²	#41×C₆₇	1	1	yes	characteristic
324	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
325	C₂³	—	4	2	no	—
326	C₂³	—	8	2	no	—
327	C₂³	—	8	2	no	—
328	C₂³	—	8	2	no	—
329	C₂³	#121×C₆₇	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	8	2	no	—
334	Q₈	—	8	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
351	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
352	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
353	C₂×C₄	#135×C₆₇	1	2	yes	—
354	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
355	C₂×C₄	#137×C₆₇	1	2	yes	—
356	C₂×C₄	#137×C₆₇	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	4	no	—
369	C₂²	#464×C₆₇	1	2	yes	—
370	C₂²	#468×C₆₇	1	2	yes	—
371	C₂²	#472×C₆₇	1	2	yes	—
372	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	2	no	—
378	C₄	#464×C₆₇	1	2	yes	—
379	C₄	#468×C₆₇	1	2	yes	—
380	C₄	C₂×#135×C₆₇	1	1	yes	characteristic
381	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
382	C₄	C₂×#137×C₆₇	1	1	yes	characteristic
383	C₄	C₂×#137×C₆₇	1	1	yes	characteristic
384	C₂	—	16	2	no	—
385	C₂	C₆₇×#1698	1	4	yes	direct product factor
386	C₂	C₂×#464×C₆₇	1	1	yes	characteristic
387	C₂	C₂×#468×C₆₇	1	1	yes	characteristic
388	C₂	C₂×#472×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#477×C₆₇	C₂	semidirect
4. C₂×#446×C₆₇	C₂	semidirect
5. C₆₇×#1698	C₂	direct (N × H)
6. C₂×#335×C₆₇	C₂	semidirect
7. C₂×#333×C₆₇	C₂	semidirect
16. #477×C₆₇	C₂²	semidirect
20. #446×C₆₇	C₂²	semidirect
32. #335×C₆₇	C₂²	semidirect
33. #333×C₆₇	C₂²	semidirect
189. C₂×#1698	C₆₇	direct (N × H)
191. C₂×C₆₇	#1698	direct (N × H)
196. C₂×#477	C₂×C₆₇	semidirect
198. C₂×#446	C₂×C₆₇	semidirect
199. #1698	C₂×C₆₇	direct (N × H)
200. C₂×#335	C₂×C₆₇	semidirect
201. C₂×#333	C₂×C₆₇	semidirect
203. C₆₇	C₂×#1698	direct (N × H)
211. #477	C₂²×C₆₇	semidirect
215. #446	C₂²×C₆₇	semidirect
227. #335	C₂²×C₆₇	semidirect
228. #333	C₂²×C₆₇	semidirect
385. C₂	C₆₇×#1698	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×#486×C₆₇	2
C₂×#477×C₆₇	2
C₂×#460×C₆₇	2
C₂×#446×C₆₇	2
C₆₇×#1698	2
C₂×#335×C₆₇	2
C₂×#333×C₆₇	2
C₂×#331×C₆₇	2
C₂×#1698	67

Subgroups — C2×C67×#1698 #30698402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1698 #30698402