Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 6. C2×C4×Dic178 | C4 | semidirect |
| 8. #19151537 | C4 | semidirect |
| 12. #19151518 | C4 | semidirect |
| 15. C4×C4⋊Dic89 | C4 | semidirect |
| 181. C89 | #11715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023520 | 2 |
| #26018566 | 2 |
| #26018275 | 2 |
| #26018272 | 2 |
| C89×#1740 | 2 |
| #11715 | 89 |