Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 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. #20277024 | C2 | semidirect |
| 2. #20272930 | C2 | semidirect |
| 3. #20272927 | C2 | semidirect |
| 4. #20272926 | C2 | semidirect |
| 5. C2×C53×D32 | C2 | semidirect |
| 7. Dic848 | C22 | semidirect |
| 9. D1696 | C22 | semidirect |
| 10. #16810342 | C22 | semidirect |
| 54. C2×D32 | D53 | semidirect |
| 71. C53 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277024 | 2 |
| #20272930 | 2 |
| #20272927 | 2 |
| #20272926 | 2 |
| C2×C53×D32 | 2 |
| #13742 | 53 |