Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20287856 | C2 | semidirect |
| 2. #20277030 | C2 | semidirect |
| 3. #20277024 | C2 | semidirect |
| 4. C2×D1696 | C2 | semidirect |
| 5. C53×#2258 | C2 | semidirect |
| 8. #16811055 | C22 | semidirect |
| 9. C2×D848 | C22 | semidirect |
| 10. Dic848 | C22 | semidirect |
| 11. #16810462 | C22 | semidirect |
| 12. D1696 | C22 | semidirect |
| 13. D1696 | C22 | semidirect |
| 15. C53×M64 | C22 | semidirect |
| 16. C2×C32×C53 | C22 | semidirect |
| 65. #2258 | D53 | semidirect |
| 78. M64 | C2×D53 | semidirect |
| 79. C2×C32 | C2×D53 | semidirect |
| 80. C53 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287856 | 2 |
| #20277030 | 2 |
| #20277024 | 2 |
| C2×D1696 | 2 |
| C53×#2258 | 2 |
| #33982 | 53 |