Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26022041 | C2 | semidirect |
| 3. C2×#19151426 | C2 | semidirect |
| 6. #26018362 | C2 | semidirect |
| 7. C89×#1382 | C2 | semidirect |
| 21. #19151381 | C4 | semidirect |
| 42. #15667952 | C2×C4 | semidirect |
| 57. C2×C16×C89 | C2×C4 | semidirect |
| 164. #1382 | D89 | semidirect |
| 165. C89 | #12926 | semidirect |
| 207. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028849 | 2 |
| #26022041 | 2 |
| C2×#19151426 | 2 |
| C2×#19151381 | 2 |
| #26020313 | 2 |
| #26018362 | 2 |
| C89×#1382 | 2 |
| #12926 | 89 |