Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26018429 | C2 | semidirect |
| 5. C4×D16×C89 | C2 | semidirect |
| 26. D16×C89 | D4 | semidirect |
| 75. C4×C89 | D32 | semidirect |
| 86. C4×D16 | D89 | semidirect |
| 89. C89 | #13685 | semidirect |
| 109. D16 | D356 | semidirect |
| 159. 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 |
| #26018429 | 2 |
| C4×D16×C89 | 2 |
| #13685 | 89 |