Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 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. Q16×Dic178 | C2 | semidirect |
| 5. #26018311 | C2 | semidirect |
| 6. #26018232 | C2 | semidirect |
| 7. C89×#1332 | C2 | semidirect |
| 75. Q16×C89 | SD16 | semidirect |
| 103. Dic178 | SD32 | semidirect |
| 134. #1332 | D89 | semidirect |
| 135. C89 | #12354 | semidirect |
| 189. Q16 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic178 | 2 |
| #26022476 | 2 |
| #26022292 | 2 |
| #26019613 | 2 |
| #26018311 | 2 |
| #26018232 | 2 |
| C89×#1332 | 2 |
| #12354 | 89 |