Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26029335 | C2 | semidirect |
| 3. #26020268 | C2 | semidirect |
| 6. #26018112 | C2 | semidirect |
| 7. C89×#1301 | C2 | semidirect |
| 12. #19151809 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 189. #1301 | D89 | semidirect |
| 191. C89 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029726 | 2 |
| #26029335 | 2 |
| #26020268 | 2 |
| #26018813 | 2 |
| #26018650 | 2 |
| #26018112 | 2 |
| C89×#1301 | 2 |
| #9310 | 89 |