Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22599278 | C2 | semidirect |
| 3. #22589318 | C2 | semidirect |
| 4. #22587008 | C2 | semidirect |
| 5. #22587007 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#3208 | C2 | semidirect |
| 48. C4⋊(C71⋊C8) | D4 | semidirect |
| 56. C4⋊Q8×C71 | D4 | semidirect |
| 57. C4⋊Q8×C71 | D4 | semidirect |
| 69. C4⋊C8×C71 | D4 | semidirect |
| 95. C4×Dic71 | SD16 | semidirect |
| 200. #3208 | D71 | semidirect |
| 206. C71 | #10290 | semidirect |
| 238. C4⋊Q8 | C22⋊D71 | semidirect |
| 239. C4⋊Q8 | C22⋊D71 | semidirect |
| 265. C4⋊C8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22596734 | 2 |
| #22589318 | 2 |
| #22587008 | 2 |
| #22587007 | 2 |
| #22586172 | 2 |
| C71×#3208 | 2 |
| #10290 | 71 |