Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 70 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. #16811520 | C4 | semidirect |
| 11. C2×#13133153 | C4 | semidirect |
| 14. C2×#108×C53 | C4 | semidirect |
| 140. C2×#108 | #6157 | semidirect |
| 147. C53 | #7256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811520 | 2 |
| C2×#16811491 | 2 |
| #20274754 | 2 |
| #7256 | 53 |