Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1998 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1998 conjugacy classes of subgroups — too many to draw. Only its 320 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 |
|---|---|---|
| 2. #20289904 | C2 | semidirect |
| 11. C22×C4⋊Dic53 | C4 | semidirect |
| 12. C22×#11719919 | C4 | semidirect |
| 14. C2×C4⋊C4×D53 | C4 | semidirect |
| 16. C22×C4⋊C4×C53 | C4 | semidirect |
| 158. C22×C4⋊C4 | #6157 | semidirect |
| 163. C53 | #14342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811566 | 2 |
| #20289904 | 2 |
| #20289889 | 2 |
| C22×C4⋊C4×D53 | 2 |
| #14342 | 53 |