Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×Dic424 | C2 | semidirect |
| 4. #20272917 | C2 | semidirect |
| 5. #20272897 | C2 | semidirect |
| 7. C4×C32×C53 | C2 | semidirect |
| 12. #16810462 | C4 | direct (N × H) |
| 25. Dic424 | C2×C4 | semidirect |
| 36. C32×C53 | C2×C4 | semidirect |
| 76. C4×C53 | SD64 | semidirect |
| 88. C4×C32 | D53 | semidirect |
| 105. C53 | C4×SD64 | semidirect |
| 122. C32 | C4×D53 | semidirect |
| 164. C4 | #16810462 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810462 | 2 |
| C4×Dic424 | 2 |
| C4×D848 | 2 |
| #20272917 | 2 |
| #20272897 | 2 |
| #20272894 | 2 |
| C4×C32×C53 | 2 |
| C4×SD64 | 53 |