Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #26018358 | C2 | semidirect |
| 5. #26018357 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#1384 | C2 | semidirect |
| 14. #19151633 | C4 | semidirect |
| 16. #106×D89 | C4 | semidirect |
| 157. #1384 | D89 | semidirect |
| 158. C89 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028844 | 2 |
| #26021872 | 2 |
| #26020295 | 2 |
| #26018358 | 2 |
| #26018357 | 2 |
| #26018353 | 2 |
| C89×#1384 | 2 |
| #12873 | 89 |