Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26020055 | C2 | semidirect |
| 5. #26020054 | C2 | semidirect |
| 6. #26018381 | C2 | semidirect |
| 7. C89×#1395 | C2 | semidirect |
| 8. C2×#15668020 | C4 | semidirect |
| 15. #19151621 | C4 | semidirect |
| 18. #19151564 | C4 | semidirect |
| 21. C2×#15667922 | C4 | semidirect |
| 22. #19151396 | C4 | semidirect |
| 23. #19151394 | C4 | semidirect |
| 212. #1395 | D89 | semidirect |
| 213. C89 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028967 | 2 |
| #26021935 | 2 |
| #26021915 | 2 |
| #26020055 | 2 |
| #26020054 | 2 |
| #26018381 | 2 |
| C89×#1395 | 2 |
| #12634 | 89 |