Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021233 | C2 | semidirect |
| 3. #26018982 | C2 | semidirect |
| 5. #26018889 | C2 | semidirect |
| 7. C89×#1506 | C2 | semidirect |
| 12. #19152321 | C4 | semidirect |
| 13. Q8×D356 | C4 | semidirect |
| 212. #1506 | D89 | semidirect |
| 214. C89 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034663 | 2 |
| #26021233 | 2 |
| #26018982 | 2 |
| #26018975 | 2 |
| #26018889 | 2 |
| #26018759 | 2 |
| C89×#1506 | 2 |
| #8496 | 89 |