Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 13. #19151418 | C4 | semidirect |
| 103. C89 | #12660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151418 | 2 |
| C2×#19151376 | 2 |
| #26019940 | 2 |
| #26018335 | 2 |
| C2×#347×C89 | 2 |
| #12660 | 89 |