Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
350 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 107 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. #19151725 | C4 | semidirect |
| 12. #19151722 | C4 | semidirect |
| 157. C89 | #8681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029182 | 2 |
| #26020382 | 2 |
| #26018998 | 2 |
| #26018817 | 2 |
| #26018815 | 2 |
| #26018112 | 2 |
| C89×#1286 | 2 |
| #8681 | 89 |