Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
272 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #26018286 | C2 | semidirect |
| 102. C89 | #11914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030911 | 2 |
| #26021857 | 2 |
| #26018286 | 2 |
| C89×#2166 | 2 |
| #11914 | 89 |