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. #26022507 | C2 | semidirect |
| 4. #26018302 | C2 | semidirect |
| 5. #26018216 | C2 | semidirect |
| 6. #26018206 | C2 | semidirect |
| 7. C89×#2207 | C2 | semidirect |
| 84. Q16×C89 | D8 | semidirect |
| 112. D356 | SD32 | semidirect |
| 148. #2207 | D89 | semidirect |
| 153. C89 | #12318 | semidirect |
| 218. Q16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D356 | 2 |
| #26022507 | 2 |
| #26019604 | 2 |
| #26018302 | 2 |
| #26018216 | 2 |
| #26018206 | 2 |
| C89×#2207 | 2 |
| #12318 | 89 |