Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 88. #10623494 | #108 | semidirect |
| 112. C89 | #8828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020390 | 2 |
| #26019010 | 2 |
| #26019007 | 2 |
| C2×#19151320 | 2 |
| C89×#1848 | 2 |
| #8828 | 89 |