Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22598872 | C2 | semidirect |
| 5. #22586445 | C2 | semidirect |
| 6. #22586427 | C2 | semidirect |
| 7. C71×#1384 | C2 | semidirect |
| 30. C2×Dic284 | Q8 | semidirect |
| 32. C2×D568 | Q8 | semidirect |
| 162. #1384 | D71 | semidirect |
| 164. C71 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598872 | 2 |
| #22590075 | 2 |
| C2×#17985810 | 2 |
| #22589236 | 2 |
| #22586445 | 2 |
| #22586427 | 2 |
| C71×#1384 | 2 |
| #13374 | 71 |