Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26031251 | C2 | semidirect |
| 3. #26018721 | C2 | semidirect |
| 4. #26018673 | C2 | semidirect |
| 5. #26018605 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#3235 | C2 | semidirect |
| 202. #3235 | D89 | semidirect |
| 209. C89 | #10121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031251 | 2 |
| #26030720 | 2 |
| #26018721 | 2 |
| #26018673 | 2 |
| #26018605 | 2 |
| #26018125 | 2 |
| C89×#3235 | 2 |
| #10121 | 89 |