Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 384 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×D356 | C2 | semidirect |
| 2. #26022508 | C2 | semidirect |
| 3. #26022292 | C2 | semidirect |
| 5. #26018300 | C2 | semidirect |
| 6. #26018208 | C2 | semidirect |
| 7. C89×#1332 | C2 | semidirect |
| 86. Q16×C89 | D8 | semidirect |
| 112. D356 | SD32 | semidirect |
| 151. #1332 | D89 | semidirect |
| 153. C89 | #12318 | semidirect |
| 218. Q16 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D356 | 2 |
| #26022508 | 2 |
| #26022292 | 2 |
| #26019608 | 2 |
| #26018300 | 2 |
| #26018208 | 2 |
| C89×#1332 | 2 |
| #12318 | 89 |