Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #26018200 | C2 | semidirect |
| 5. #26018181 | C2 | semidirect |
| 6. #26018181 | C2 | semidirect |
| 7. C89×#1326 | C2 | semidirect |
| 224. #1326 | D89 | semidirect |
| 227. C89 | #11543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024532 | 2 |
| #26018577 | 2 |
| #323×D89 | 2 |
| #26018200 | 2 |
| #26018181 | 2 |
| C89×#1326 | 2 |
| #11543 | 89 |