Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 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. C2×#19151995 | C2 | semidirect |
| 5. #26018352 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C89×#1383 | C2 | semidirect |
| 29. C2×Dic356 | Q8 | semidirect |
| 31. C2×D712 | Q8 | semidirect |
| 154. #1383 | D89 | semidirect |
| 156. C89 | #13371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151995 | 2 |
| C2×#19151409 | 2 |
| C2×#19151407 | 2 |
| #26021138 | 2 |
| #26018352 | 2 |
| #26018333 | 2 |
| C89×#1383 | 2 |
| #13371 | 89 |