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 |
|---|---|---|
| 5. C2×#15668012 | C4 | semidirect |
| 9. #19151528 | C4 | semidirect |
| 13. #19151464 | C4 | semidirect |
| 161. C89 | #11694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026018 | 2 |
| #26018566 | 2 |
| #26018251 | 2 |
| C89×#1740 | 2 |
| #11694 | 89 |