Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26031460 | C2 | semidirect |
| 5. #26018853 | C2 | semidirect |
| 6. #26018763 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 185. #1300 | D89 | semidirect |
| 186. C89 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031460 | 2 |
| #26030627 | 2 |
| #26026195 | 2 |
| #26018965 | 2 |
| #26018853 | 2 |
| #26018763 | 2 |
| C89×#1300 | 2 |
| #10097 | 89 |