Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. C2×Dic848 | C2 | semidirect |
| 3. C2×#16810463 | C2 | semidirect |
| 4. Q64×D53 | C2 | direct (N × H) |
| 6. C2×C53×Q64 | C2 | semidirect |
| 13. Dic848 | C22 | semidirect |
| 14. #16810463 | C22 | semidirect |
| 18. C53×Q64 | C22 | semidirect |
| 75. C2×D53 | Q64 | direct (N × H) |
| 86. C2×Q64 | D53 | direct (N × H) |
| 88. C2×C53 | C2×Q64 | semidirect |
| 90. D53 | C2×Q64 | direct (N × H) |
| 100. Q64 | C2×D53 | direct (N × H) |
| 104. C53 | C22×Q64 | semidirect |
| 167. C2 | Q64×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D53 | 2 |
| C2×Dic848 | 2 |
| C2×#16810463 | 2 |
| Q64×D53 | 2 |
| C2×C32×D53 | 2 |
| C2×C53×Q64 | 2 |
| C22×Q64 | 53 |