Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
870 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 870 conjugacy classes of subgroups — too many to draw. Only its 276 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. #16811499 | C4 | semidirect |
| 120. C53 | #10705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719936 | 2 |
| C2×#16811499 | 2 |
| C2×#97×D53 | 2 |
| #10705 | 53 |