Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
700 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 700 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 |
|---|---|---|
| 6. C2×#15668010 | C4 | semidirect |
| 11. #19151505 | C4 | semidirect |
| 164. C89 | #9462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023892 | 2 |
| #26020176 | 2 |
| #26018784 | 2 |
| #26018104 | 2 |
| C89×#2310 | 2 |
| #9462 | 89 |