Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 2. #26022025 | C2 | semidirect |
| 3. #26022024 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C89×#1389 | C2 | semidirect |
| 19. #19151379 | C4 | semidirect |
| 41. #15667952 | C2×C4 | semidirect |
| 54. M32×C89 | C2×C4 | semidirect |
| 155. #1389 | D89 | semidirect |
| 156. C89 | #12932 | semidirect |
| 195. M32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028840 | 2 |
| #26022025 | 2 |
| #26022024 | 2 |
| C2×#19151379 | 2 |
| #26020291 | 2 |
| #26018366 | 2 |
| C89×#1389 | 2 |
| #12932 | 89 |