Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×#15667952 | C2 | semidirect |
| 3. C2×#19151398 | C2 | semidirect |
| 4. #26018343 | C2 | semidirect |
| 5. C89×#1808 | C2 | semidirect |
| 12. #19151834 | C4 | semidirect |
| 33. C2×#13083549 | D4 | semidirect |
| 149. #1808 | D89 | semidirect |
| 151. C89 | #13061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667952 | 2 |
| C2×#19151834 | 2 |
| C2×#19151398 | 2 |
| #26018343 | 2 |
| C89×#1808 | 2 |
| #13061 | 89 |