Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26021835 | C2 | semidirect |
| 2. #26021704 | C2 | semidirect |
| 4. #26020964 | C2 | semidirect |
| 6. #26020493 | C2 | semidirect |
| 7. #26020470 | C2 | semidirect |
| 8. #26020392 | C2 | semidirect |
| 9. C89×#2102 | C2 | semidirect |
| 136. #2102 | D89 | semidirect |
| 144. C89 | #32703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021835 | 2 |
| #26021704 | 2 |
| #26021539 | 2 |
| #26020964 | 2 |
| #26020613 | 2 |
| #26020493 | 2 |
| #26020470 | 2 |
| #26020392 | 2 |
| C89×#2102 | 2 |
| #32703 | 89 |