Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22598880 | C2 | semidirect |
| 5. #22586450 | C2 | semidirect |
| 6. #22586428 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 31. C2×D568 | Q8 | semidirect |
| 164. #1382 | D71 | semidirect |
| 166. C71 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598880 | 2 |
| #22590055 | 2 |
| C2×#17985801 | 2 |
| #22589248 | 2 |
| #22586450 | 2 |
| #22586428 | 2 |
| C71×#1382 | 2 |
| #13369 | 71 |