Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
954 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26034666 | C2 | semidirect |
| 2. #26031640 | C2 | semidirect |
| 4. #26019393 | C2 | semidirect |
| 5. #26019374 | C2 | semidirect |
| 6. #26019331 | C2 | semidirect |
| 7. #26019312 | C2 | semidirect |
| 8. #26018706 | C2 | semidirect |
| 9. C89×#1560 | C2 | semidirect |
| 198. #1560 | D89 | semidirect |
| 200. C89 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034666 | 2 |
| #26031640 | 2 |
| #26030678 | 2 |
| #26019393 | 2 |
| #26019374 | 2 |
| #26019331 | 2 |
| #26019312 | 2 |
| #26018706 | 2 |
| C89×#1560 | 2 |
| #18688 | 89 |