Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
310 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. #16811551 | C4 | semidirect |
| 11. #16811510 | C4 | semidirect |
| 15. #16810451 | C4 | semidirect |
| 16. #16810448 | C4 | semidirect |
| 17. C53×#367 | C4 | semidirect |
| 108. #367 | #6157 | semidirect |
| 112. C53 | #12671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811551 | 2 |
| C2×#16811510 | 2 |
| #20290519 | 2 |
| #20289776 | 2 |
| #20276498 | 2 |
| #12671 | 53 |