Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 12. #19151625 | C4 | semidirect |
| 13. #19151625 | C4 | semidirect |
| 18. C4×#13083558 | C4 | semidirect |
| 19. C2×#15667923 | C4 | semidirect |
| 174. C89 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028903 | 2 |
| #26020356 | 2 |
| #26018382 | 2 |
| #26018380 | 2 |
| #26018374 | 2 |
| #26018372 | 2 |
| C89×#1827 | 2 |
| #12865 | 89 |