Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26028202 | C2 | semidirect |
| 5. #26018077 | C2 | semidirect |
| 6. #26018074 | C2 | semidirect |
| 7. C89×#1271 | C2 | semidirect |
| 97. C4⋊Dic89 | SD16 | semidirect |
| 216. #1271 | D89 | semidirect |
| 217. C89 | #7747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028202 | 2 |
| #26021487 | 2 |
| #26021486 | 2 |
| #26021342 | 2 |
| #26018077 | 2 |
| #26018074 | 2 |
| C89×#1271 | 2 |
| #7747 | 89 |