Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26031003 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26018611 | C2 | semidirect |
| 4. #26018129 | C2 | semidirect |
| 5. C89×#1780 | C2 | semidirect |
| 169. #1780 | D89 | semidirect |
| 172. C89 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031003 | 2 |
| #26029504 | 2 |
| #26018611 | 2 |
| #26018129 | 2 |
| C89×#1780 | 2 |
| #9974 | 89 |