Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 10. #16811548 | C4 | direct (N × H) |
| 16. #16810398 | C4 | semidirect |
| 17. #16810398 | C4 | semidirect |
| 18. C4×#11719908 | C4 | semidirect |
| 19. C4×C16×C53 | C4 | semidirect |
| 65. C16×C53 | C42 | semidirect |
| 67. #11719908 | C42 | semidirect |
| 95. C4×C53 | #365 | semidirect |
| 121. C4×C16 | #6157 | semidirect |
| 124. C53 | C4×#365 | semidirect |
| 172. C16 | C4×#6157 | semidirect |
| 202. C4 | #16811548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811548 | 2 |
| C4×#13133287 | 2 |
| C4×#13133285 | 2 |
| #20289780 | 2 |
| C4×#13133156 | 2 |
| C4×#365 | 53 |