Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20291476 | C2 | semidirect |
| 3. #20291025 | C2 | semidirect |
| 5. #20289783 | C2 | semidirect |
| 6. #20289764 | C2 | semidirect |
| 24. C2×#13133163 | C4 | semidirect |
| 25. C2×#13133162 | C4 | semidirect |
| 26. C2×#13133160 | C4 | semidirect |
| 28. C2×Q32×C53 | C4 | semidirect |
| 195. C2×Q32 | #6157 | semidirect |
| 210. C53 | #13034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291476 | 2 |
| #20291037 | 2 |
| #20291025 | 2 |
| #20290874 | 2 |
| #20289783 | 2 |
| #20289764 | 2 |
| C2×#16811065 | 2 |
| #13034 | 53 |