Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20274753 | C2 | semidirect |
| 4. #20272621 | C2 | semidirect |
| 5. C53×#1807 | C2 | semidirect |
| 6. C2×#13133223 | C4 | semidirect |
| 13. #16810649 | C4 | semidirect |
| 14. #16810589 | C4 | semidirect |
| 17. #16810578 | C4 | semidirect |
| 180. #1807 | D53 | semidirect |
| 209. C53 | #8629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283409 | 2 |
| #20274753 | 2 |
| #20273256 | 2 |
| #20272621 | 2 |
| C53×#1807 | 2 |
| #8629 | 53 |