Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26023418 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1508 | C2 | semidirect |
| 9. #19151931 | C4 | semidirect |
| 12. #19151748 | C4 | semidirect |
| 233. #1508 | D89 | semidirect |
| 236. C89 | #9344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26023418 | 2 |
| #26021088 | 2 |
| #26018782 | 2 |
| #26018157 | 2 |
| #26018105 | 2 |
| C89×#1508 | 2 |
| #9344 | 89 |