Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 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. C16×Dic178 | C2 | semidirect |
| 2. #26019619 | C2 | semidirect |
| 4. #26018326 | C2 | semidirect |
| 5. #26018301 | C2 | semidirect |
| 70. C16×C89 | SD16 | semidirect |
| 86. Dic178 | SD32 | semidirect |
| 117. C89 | #12441 | semidirect |
| 180. C16 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic178 | 2 |
| #26019619 | 2 |
| #26019609 | 2 |
| #26018326 | 2 |
| #26018301 | 2 |
| #26018298 | 2 |
| C89×#2248 | 2 |
| #12441 | 89 |