Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26030283 | C2 | semidirect |
| 3. #26021084 | C2 | semidirect |
| 4. #26018681 | C2 | semidirect |
| 5. #26018677 | C2 | semidirect |
| 6. #26018081 | C2 | semidirect |
| 7. C89×#2398 | C2 | semidirect |
| 219. #2398 | D89 | semidirect |
| 224. C89 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030283 | 2 |
| #26030252 | 2 |
| #26021084 | 2 |
| #26018681 | 2 |
| #26018677 | 2 |
| #26018081 | 2 |
| C89×#2398 | 2 |
| #10013 | 89 |