Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×Dic178 | C2 | semidirect |
| 2. #26022476 | C2 | semidirect |
| 4. #26019613 | C2 | semidirect |
| 5. #26018308 | C2 | semidirect |
| 6. #26018232 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 78. D8×C89 | SD16 | semidirect |
| 109. Dic178 | D16 | semidirect |
| 143. #1331 | D89 | semidirect |
| 144. C89 | #12352 | semidirect |
| 206. D8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic178 | 2 |
| #26022476 | 2 |
| #26022287 | 2 |
| #26019613 | 2 |
| #26018308 | 2 |
| #26018232 | 2 |
| C89×#1331 | 2 |
| #12352 | 89 |