Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022502 | C2 | semidirect |
| 2. #26019607 | C2 | semidirect |
| 3. #26018324 | C2 | semidirect |
| 4. #26018299 | C2 | semidirect |
| 5. D4×C16×C89 | C2 | semidirect |
| 54. C16×C89 | D8 | semidirect |
| 58. D4×C89 | D16 | semidirect |
| 95. D4×C16 | D89 | semidirect |
| 99. C89 | #12430 | semidirect |
| 148. C16 | #13083559 | semidirect |
| 157. D4 | D1424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022502 | 2 |
| #26019607 | 2 |
| #26018324 | 2 |
| #26018299 | 2 |
| D4×C16×C89 | 2 |
| #12430 | 89 |