Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. Q64×D53 | C2 | semidirect |
| 3. #20272931 | C2 | semidirect |
| 4. #20272930 | C2 | semidirect |
| 5. #20272929 | C2 | semidirect |
| 6. C64×D53 | C2 | semidirect |
| 7. C53×SD128 | C2 | semidirect |
| 10. Dic848 | C22 | semidirect |
| 15. #16810342 | C22 | semidirect |
| 16. C53×Q64 | C22 | semidirect |
| 18. C53×C64 | C22 | semidirect |
| 66. SD128 | D53 | direct (N × H) |
| 71. D53 | SD128 | direct (N × H) |
| 76. Q64 | C2×D53 | semidirect |
| 82. C64 | C2×D53 | semidirect |
| 83. C53 | C2×SD128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q64×D53 | 2 |
| D32×D53 | 2 |
| #20272931 | 2 |
| #20272930 | 2 |
| #20272929 | 2 |
| C64×D53 | 2 |
| C53×SD128 | 2 |
| C2×SD128 | 53 |