Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 496 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. #26028888 | C2 | semidirect |
| 3. #26018851 | C2 | semidirect |
| 4. #26018849 | C2 | semidirect |
| 5. #26018584 | C2 | semidirect |
| 6. #26018145 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 61. #15667923 | D4 | semidirect |
| 71. #97×C89 | D4 | semidirect |
| 225. #1300 | D89 | semidirect |
| 226. C89 | #9389 | semidirect |
| 287. #97 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028888 | 2 |
| #26025933 | 2 |
| #26018851 | 2 |
| #26018849 | 2 |
| #26018584 | 2 |
| #26018145 | 2 |
| C89×#1300 | 2 |
| #9389 | 89 |