Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26031646 | C2 | semidirect |
| 5. #26018846 | C2 | semidirect |
| 6. #26018672 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 191. #1299 | D89 | semidirect |
| 192. C89 | #10113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031646 | 2 |
| #26031195 | 2 |
| #26030627 | 2 |
| #26021091 | 2 |
| #26018846 | 2 |
| #26018672 | 2 |
| C89×#1299 | 2 |
| #10113 | 89 |