Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26031393 | C2 | semidirect |
| 4. #26021071 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1518 | C2 | semidirect |
| 186. #1518 | D89 | semidirect |
| 189. C89 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031393 | 2 |
| #26031375 | 2 |
| #26030600 | 2 |
| #26021071 | 2 |
| #26018811 | 2 |
| #26018096 | 2 |
| C89×#1518 | 2 |
| #10226 | 89 |