Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26030292 | C2 | semidirect |
| 4. #26018815 | C2 | semidirect |
| 5. #26018680 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 93. C2×D356 | Q16 | semidirect |
| 220. #1286 | D89 | semidirect |
| 221. C89 | #10002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030292 | 2 |
| #26030051 | 2 |
| #26025611 | 2 |
| #26018815 | 2 |
| #26018680 | 2 |
| #26018644 | 2 |
| C89×#1286 | 2 |
| #10002 | 89 |