Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018265 | C2 | semidirect |
| 5. #26018264 | C2 | semidirect |
| 6. #26018263 | C2 | semidirect |
| 7. C89×#1348 | C2 | semidirect |
| 8. C2×Q16×D89 | C4 | semidirect |
| 13. #19151840 | C4 | semidirect |
| 17. #19151836 | C4 | semidirect |
| 18. #107×D89 | C4 | semidirect |
| 194. #1348 | D89 | semidirect |
| 195. C89 | #11706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D89 | 2 |
| #26021861 | 2 |
| #26019967 | 2 |
| #26018265 | 2 |
| #26018264 | 2 |
| #26018263 | 2 |
| C89×#1348 | 2 |
| #11706 | 89 |