Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
646 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26021923 | C2 | semidirect |
| 3. #26021901 | C2 | semidirect |
| 4. #26020227 | C2 | semidirect |
| 5. #26018380 | C2 | semidirect |
| 6. #26018372 | C2 | semidirect |
| 7. C89×#2884 | C2 | semidirect |
| 8. C2×#15668037 | C4 | semidirect |
| 9. C22×#13083561 | C4 | semidirect |
| 17. #19151607 | C4 | semidirect |
| 18. #19151594 | C4 | semidirect |
| 249. #2884 | D89 | semidirect |
| 255. C89 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029538 | 2 |
| #26021923 | 2 |
| #26021901 | 2 |
| #26020227 | 2 |
| #26018380 | 2 |
| #26018372 | 2 |
| C89×#2884 | 2 |
| #13103 | 89 |