Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 11. #19151995 | C4 | semidirect |
| 33. #15667946 | Q8 | semidirect |
| 49. #108×C89 | Q8 | semidirect |
| 129. C89 | #13272 | semidirect |
| 162. #108 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151995 | 2 |
| C2×#19151418 | 2 |
| #26020134 | 2 |
| #26018359 | 2 |
| #26018358 | 2 |
| #26018352 | 2 |
| C89×#1383 | 2 |
| #13272 | 89 |