Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 2. C2×#19151421 | C2 | semidirect |
| 5. #26021005 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C89×#1375 | C2 | semidirect |
| 19. #19151400 | C4 | semidirect |
| 40. #15667946 | C2×C4 | semidirect |
| 54. C2×C16×C89 | C2×C4 | semidirect |
| 151. #1375 | D89 | semidirect |
| 152. C89 | #12956 | semidirect |
| 191. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151711 | 2 |
| C2×#19151421 | 2 |
| C2×#19151412 | 2 |
| #26021969 | 2 |
| #26021005 | 2 |
| #26018358 | 2 |
| C89×#1375 | 2 |
| #12956 | 89 |