Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 516 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. #26029336 | C2 | semidirect |
| 3. C4×#15667930 | C2 | semidirect |
| 6. #26018145 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 219. #1300 | D89 | semidirect |
| 220. C89 | #9032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029336 | 2 |
| #26023538 | 2 |
| C4×#15667930 | 2 |
| #26018696 | 2 |
| #26018694 | 2 |
| #26018145 | 2 |
| C89×#1300 | 2 |
| #9032 | 89 |