Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
544 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26030196 | C2 | semidirect |
| 4. #26020327 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 7. C89×#1511 | C2 | semidirect |
| 217. #1511 | D89 | semidirect |
| 220. C89 | #9984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030196 | 2 |
| #26030193 | 2 |
| #26028279 | 2 |
| #26020327 | 2 |
| #26018780 | 2 |
| #26018161 | 2 |
| C89×#1511 | 2 |
| #9984 | 89 |