Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 576 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 |
|---|---|---|
| 2. #26023364 | C2 | semidirect |
| 3. #26018761 | C2 | semidirect |
| 4. #26018144 | C2 | semidirect |
| 5. C89×#1533 | C2 | semidirect |
| 9. #19151993 | C4 | semidirect |
| 10. #19151988 | C4 | semidirect |
| 34. #15668012 | C2×C4 | semidirect |
| 35. #15668009 | C2×C4 | semidirect |
| 44. #15667923 | C2×C4 | semidirect |
| 173. #1533 | D89 | semidirect |
| 176. C89 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030716 | 2 |
| #26023364 | 2 |
| #26018761 | 2 |
| #26018144 | 2 |
| C89×#1533 | 2 |
| #9441 | 89 |