Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
482 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 10. #19151933 | C4 | semidirect |
| 11. #19151928 | C4 | semidirect |
| 219. C89 | #9526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030200 | 2 |
| #26023005 | 2 |
| #26020351 | 2 |
| #26018784 | 2 |
| #26018160 | 2 |
| #26018104 | 2 |
| C89×#1820 | 2 |
| #9526 | 89 |