Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26020105 | C2 | semidirect |
| 2. #26018078 | C2 | semidirect |
| 143. C89 | #7635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020105 | 2 |
| #26018078 | 2 |
| #26018073 | 2 |
| C4×#124×C89 | 2 |
| #7635 | 89 |