Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 110. #11719940 | Q16 | semidirect |
| 243. C53 | #9248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291516 | 2 |
| #20290907 | 2 |
| #20290228 | 2 |
| #20290045 | 2 |
| #20289585 | 2 |
| #20289560 | 2 |
| C2×#16810832 | 2 |
| #9248 | 53 |