Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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. C4×#15667947 | C2 | semidirect |
| 3. #26019013 | C2 | semidirect |
| 6. #26018123 | C2 | semidirect |
| 7. C89×#1291 | C2 | semidirect |
| 173. #1291 | D89 | semidirect |
| 174. C89 | #8693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029221 | 2 |
| C4×#15667947 | 2 |
| #26019013 | 2 |
| #26018860 | 2 |
| #26018857 | 2 |
| #26018123 | 2 |
| C89×#1291 | 2 |
| #8693 | 89 |