Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
180 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. C2×#16810463 | C2 | semidirect |
| 5. #20272918 | C2 | semidirect |
| 6. #20272909 | C2 | semidirect |
| 7. C53×#1420 | C2 | semidirect |
| 93. #1420 | D53 | semidirect |
| 112. C53 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| #20277010 | 2 |
| #20276841 | 2 |
| #20276837 | 2 |
| #20272918 | 2 |
| #20272909 | 2 |
| C53×#1420 | 2 |
| #13701 | 53 |