Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 3. #26021073 | C2 | semidirect |
| 5. #26018112 | C2 | semidirect |
| 6. #26018082 | C2 | semidirect |
| 7. C89×#1546 | C2 | semidirect |
| 10. #19152001 | C4 | semidirect |
| 11. #19151946 | C4 | semidirect |
| 185. #1546 | D89 | semidirect |
| 189. C89 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031373 | 2 |
| #26028969 | 2 |
| #26021073 | 2 |
| #26018813 | 2 |
| #26018112 | 2 |
| #26018082 | 2 |
| C89×#1546 | 2 |
| #9291 | 89 |