Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 7. C2×#13133128 | C4 | semidirect |
| 8. #16810489 | C4 | semidirect |
| 10. #16810416 | C4 | semidirect |
| 14. C53×#353 | C4 | semidirect |
| 150. #353 | Dic53 | semidirect |
| 151. C53 | #7504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20275540 | 2 |
| C2×C53×#353 | 2 |
| #7504 | 53 |