Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 9. C8×#88322 | C4 | semidirect |
| 57. C8×C53 | #107 | semidirect |
| 58. #88322 | #107 | semidirect |
| 88. C53 | #8818 | semidirect |
| 134. C8 | #13133150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274875 | 2 |
| #20274874 | 2 |
| C2×C8×#88322 | 2 |
| C53×#1845 | 2 |
| #8818 | 53 |