Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1598 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1598 conjugacy classes of subgroups — too many to draw. Only its 440 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. #16811559 | C4 | semidirect |
| 12. C42×Dic53 | C4 | semidirect |
| 13. C42×Dic53 | C4 | semidirect |
| 14. C42×Dic53 | C4 | semidirect |
| 15. C43×C53 | C4 | semidirect |
| 121. C43 | #6157 | semidirect |
| 122. C53 | #13757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811559 | 2 |
| #20289891 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| C43×D53 | 2 |
| #13757 | 53 |