Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022508 | C2 | semidirect |
| 2. C16×D356 | C2 | semidirect |
| 3. #26019618 | C2 | semidirect |
| 5. #26018300 | C2 | semidirect |
| 6. #26018297 | C2 | semidirect |
| 7. C89×#1372 | C2 | semidirect |
| 73. C16×C89 | D8 | semidirect |
| 87. D356 | SD32 | semidirect |
| 122. #1372 | D89 | semidirect |
| 125. C89 | #12432 | semidirect |
| 191. C16 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022508 | 2 |
| C16×D356 | 2 |
| #26019618 | 2 |
| #26019608 | 2 |
| #26018300 | 2 |
| #26018297 | 2 |
| C89×#1372 | 2 |
| #12432 | 89 |