Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26028630 | C2 | semidirect |
| 3. #26018112 | C2 | semidirect |
| 4. #26018085 | C2 | semidirect |
| 30. C4⋊Q8×C89 | Q8 | semidirect |
| 31. #127×C89 | Q8 | semidirect |
| 132. C89 | #10362 | semidirect |
| 149. C4⋊Q8 | Dic178 | semidirect |
| 150. #127 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028630 | 2 |
| #26018812 | 2 |
| #26018112 | 2 |
| #26018085 | 2 |
| C89×#1962 | 2 |
| #10362 | 89 |