Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26032601 | C2 | semidirect |
| 2. #26022527 | C2 | semidirect |
| 3. #26022431 | C2 | semidirect |
| 4. #26022389 | C2 | semidirect |
| 5. #26022335 | C2 | semidirect |
| 6. C16×D356 | C2 | semidirect |
| 7. #366×D89 | C2 | semidirect |
| 8. C4×D16×C89 | C2 | semidirect |
| 78. C16×C89 | #41 | semidirect |
| 91. D356 | D16 | semidirect |
| 125. C4×D16 | D89 | semidirect |
| 128. C89 | #33901 | semidirect |
| 198. C16 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032601 | 2 |
| #26022527 | 2 |
| #26022431 | 2 |
| #26022389 | 2 |
| #26022335 | 2 |
| C16×D356 | 2 |
| #366×D89 | 2 |
| C4×D16×C89 | 2 |
| #33901 | 89 |