Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
270 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 270 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×#19151433 | C2 | semidirect |
| 2. #26022502 | C2 | semidirect |
| 3. C4×#15667918 | C2 | semidirect |
| 4. C89×#2246 | C2 | semidirect |
| 19. #15667918 | D4 | semidirect |
| 61. C4×C89 | D32 | semidirect |
| 71. #2246 | D89 | semidirect |
| 73. C89 | #13725 | semidirect |
| 130. C4 | #19151433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151433 | 2 |
| #26022502 | 2 |
| C4×#15667918 | 2 |
| C89×#2246 | 2 |
| #13725 | 89 |