Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. #26018263 | C2 | semidirect |
| 5. C22×Dic356 | C4 | semidirect |
| 10. #19151839 | C4 | semidirect |
| 12. C2×#15667946 | C4 | semidirect |
| 152. C89 | #11706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151839 | 2 |
| #26021863 | 2 |
| #26018263 | 2 |
| C89×#1735 | 2 |
| #11706 | 89 |