Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 18. #19151402 | C4 | semidirect |
| 143. C89 | #12957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151705 | 2 |
| C2×#19151422 | 2 |
| #26021972 | 2 |
| #26021003 | 2 |
| #26018358 | 2 |
| #26018331 | 2 |
| C2×#362×C89 | 2 |
| #12957 | 89 |