Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1326 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 491 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 |
|---|---|---|
| 5. #16810491 | C4 | semidirect |
| 10. C53×#384 | C4 | semidirect |
| 34. C42×C53 | C42 | semidirect |
| 70. #384 | Dic53 | semidirect |
| 74. C53 | #13830 | semidirect |
| 99. C42 | C4×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| #20272947 | 2 |
| C2×C53×#384 | 2 |
| #13830 | 53 |