Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
376 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 111 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. #19151705 | C4 | semidirect |
| 139. C89 | #12827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029120 | 2 |
| #26022017 | 2 |
| C2×#19151414 | 2 |
| #26020375 | 2 |
| #26018367 | 2 |
| #26018353 | 2 |
| C89×#2141 | 2 |
| #12827 | 89 |