Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
748 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #26018590 | C2 | semidirect |
| 3. #26018179 | C2 | semidirect |
| 4. C89×#1460 | C2 | semidirect |
| 190. #1460 | D89 | semidirect |
| 192. C89 | #11561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023608 | 2 |
| #26018590 | 2 |
| #26018179 | 2 |
| C89×#1460 | 2 |
| #11561 | 89 |