Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
128 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26018388 | C2 | semidirect |
| 2. #26018320 | C2 | semidirect |
| 60. C89 | #7390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018388 | 2 |
| #26018320 | 2 |
| C89×#2177 | 2 |
| #7390 | 89 |