Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
268 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26018085 | C2 | semidirect |
| 13. C4⋊Q8×C89 | C8 | semidirect |
| 14. #127×C89 | C8 | semidirect |
| 87. C89 | #7106 | semidirect |
| 95. C4⋊Q8 | #10623494 | semidirect |
| 96. #127 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018085 | 2 |
| C89×#1962 | 2 |
| #7106 | 89 |