Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26028671 | C2 | semidirect |
| 3. #26018851 | C2 | semidirect |
| 4. #26018144 | C2 | semidirect |
| 5. C89×#1464 | C2 | semidirect |
| 44. #15667923 | D4 | semidirect |
| 192. #1464 | D89 | semidirect |
| 194. C89 | #9387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028671 | 2 |
| #26025939 | 2 |
| #26018851 | 2 |
| #26018144 | 2 |
| C89×#1464 | 2 |
| #9387 | 89 |