Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. #26020288 | C2 | semidirect |
| 3. #26020279 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 8. C2×#15668020 | C4 | semidirect |
| 17. #19151626 | C4 | semidirect |
| 18. #19151566 | C4 | semidirect |
| 20. #19151556 | C4 | semidirect |
| 220. #1305 | D89 | semidirect |
| 221. C89 | #8627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028942 | 2 |
| #26020288 | 2 |
| #26020279 | 2 |
| #26018796 | 2 |
| #26018793 | 2 |
| #26018157 | 2 |
| C89×#1305 | 2 |
| #8627 | 89 |