Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 10. #19152003 | C4 | semidirect |
| 11. #19151949 | C4 | semidirect |
| 172. C89 | #9298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031405 | 2 |
| #26023000 | 2 |
| #26021233 | 2 |
| #26018936 | 2 |
| #26018817 | 2 |
| #26018111 | 2 |
| C89×#1274 | 2 |
| #9298 | 89 |