Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
378 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#17985826 | C2 | semidirect |
| 2. C2×#17985824 | C2 | semidirect |
| 6. #22586418 | C2 | semidirect |
| 7. C71×#1846 | C2 | semidirect |
| 150. #1846 | D71 | semidirect |
| 152. C71 | #13528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985826 | 2 |
| C2×#17985824 | 2 |
| C2×#17985799 | 2 |
| #22589206 | 2 |
| #22586418 | 2 |
| C71×#1846 | 2 |
| #13528 | 71 |