Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
150 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 27. #15667918 | Q8 | semidirect |
| 31. C32×C89 | Q8 | semidirect |
| 77. C89 | #13734 | semidirect |
| 101. C32 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022529 | 2 |
| #26022526 | 2 |
| #26018453 | 2 |
| #26018452 | 2 |
| #26018451 | 2 |
| #26018385 | 2 |
| C89×#1424 | 2 |
| #13734 | 89 |