Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 12. Dic848 | C4 | semidirect |
| 13. #16810463 | C4 | semidirect |
| 15. C53×Q64 | C4 | semidirect |
| 57. #6157 | Q64 | direct (N × H) |
| 74. Q64 | #6157 | direct (N × H) |
| 80. C53 | C4×Q64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×#6157 | 2 |
| #20289876 | 2 |
| #20289865 | 2 |
| C32×#6157 | 2 |
| Q64×D53 | 2 |
| C4×Q64 | 53 |