Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
310 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 13. #16810400 | C4 | semidirect |
| 111. C53 | #12596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810400 | 2 |
| #20274403 | 2 |
| #20272799 | 2 |
| #20272796 | 2 |
| C53×#1377 | 2 |
| #12596 | 53 |