Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 542 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. #26023139 | C2 | semidirect |
| 4. #26020349 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 13. #19151640 | C4 | semidirect |
| 14. #19151604 | C4 | semidirect |
| 208. #1305 | D89 | semidirect |
| 210. C89 | #9367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030193 | 2 |
| #26023139 | 2 |
| #26021087 | 2 |
| #26020349 | 2 |
| #26018769 | 2 |
| #26018137 | 2 |
| C89×#1305 | 2 |
| #9367 | 89 |