Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1054 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 360 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. #20290434 | C2 | semidirect |
| 6. C4×#11719936 | C4 | semidirect |
| 20. #13133272 | C2×C4 | semidirect |
| 21. C4×#88324 | C2×C4 | semidirect |
| 112. C53 | #20365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719936 | 2 |
| #20290434 | 2 |
| #20290379 | 2 |
| #376×D53 | 2 |
| #20365 | 53 |