Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 13. #19151976 | C4 | semidirect |
| 168. C89 | #13262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151976 | 2 |
| C2×#19151418 | 2 |
| C2×#19151415 | 2 |
| C2×#19151414 | 2 |
| #26021971 | 2 |
| #26020133 | 2 |
| C89×#2141 | 2 |
| #13262 | 89 |