Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
314 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 16. #19151403 | C4 | semidirect |
| 136. C89 | #13154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151415 | 2 |
| #26021973 | 2 |
| #26021123 | 2 |
| #26021005 | 2 |
| #26018358 | 2 |
| #26018351 | 2 |
| C2×#347×C89 | 2 |
| #13154 | 89 |