Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
448 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 8. C2×#15668010 | C4 | semidirect |
| 14. #19151519 | C4 | semidirect |
| 15. #19151517 | C4 | semidirect |
| 18. #19151462 | C4 | semidirect |
| 198. C89 | #11717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026072 | 2 |
| #26019983 | 2 |
| #26018563 | 2 |
| #26018274 | 2 |
| #26018273 | 2 |
| #26018272 | 2 |
| C89×#1351 | 2 |
| #11717 | 89 |