Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022454 | C2 | semidirect |
| 4. #26018263 | C2 | semidirect |
| 6. #26018192 | C2 | semidirect |
| 7. C89×#2087 | C2 | semidirect |
| 156. #2087 | D89 | semidirect |
| 160. C89 | #12293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031604 | 2 |
| #26022454 | 2 |
| #26022437 | 2 |
| #26018263 | 2 |
| #26018260 | 2 |
| #26018192 | 2 |
| C89×#2087 | 2 |
| #12293 | 89 |