Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
250 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. C2×#19151435 | C2 | semidirect |
| 3. C4×#15667918 | C2 | semidirect |
| 4. C89×#2247 | C2 | semidirect |
| 19. #15667918 | D4 | semidirect |
| 59. C4×C89 | SD64 | semidirect |
| 67. #2247 | D89 | semidirect |
| 70. C89 | #13727 | semidirect |
| 125. C4 | #19151435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151435 | 2 |
| #26022502 | 2 |
| C4×#15667918 | 2 |
| C89×#2247 | 2 |
| #13727 | 89 |