Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
364 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26018241 | C2 | semidirect |
| 5. #26018240 | C2 | semidirect |
| 6. #26018239 | C2 | semidirect |
| 7. C89×#1340 | C2 | semidirect |
| 8. C2×Q16×D89 | C4 | semidirect |
| 12. #19151857 | C4 | semidirect |
| 14. #19151853 | C4 | semidirect |
| 18. #19151633 | C4 | semidirect |
| 184. #1340 | D89 | semidirect |
| 185. C89 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029905 | 2 |
| #26021871 | 2 |
| #26020297 | 2 |
| #26018241 | 2 |
| #26018240 | 2 |
| #26018239 | 2 |
| C89×#1340 | 2 |
| #11869 | 89 |