Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1350 conjugacy classes of subgroups; only the 504 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 504 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. #20290647 | C2 | semidirect |
| 37. C42×C53 | M16 | semidirect |
| 62. C4×C53 | #423 | semidirect |
| 80. C53 | #20791 | semidirect |
| 109. C42 | #11719936 | semidirect |
| 133. C4 | #16811627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811627 | 2 |
| #20290647 | 2 |
| C43×D53 | 2 |
| #20791 | 53 |