Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
710 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 180 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. #16811643 | C4 | semidirect |
| 156. C53 | #7910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811643 | 2 |
| #20289553 | 2 |
| C2×#16810469 | 2 |
| #7910 | 53 |