Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
142 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 25 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 |
|---|---|---|
| 5. #19151978 | C4 | semidirect |
| 8. #19151319 | C4 | semidirect |
| 64. C89 | #7528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019921 | 2 |
| #26018419 | 2 |
| C89×#1409 | 2 |
| #7528 | 89 |