Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
314 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 15. #19151401 | C4 | semidirect |
| 136. C89 | #13154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151413 | 2 |
| #26021971 | 2 |
| C2×#19151376 | 2 |
| #26021123 | 2 |
| #26018357 | 2 |
| #26018352 | 2 |
| C89×#1946 | 2 |
| #13154 | 89 |