Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1566 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 440 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 |
|---|---|---|
| 6. #16811568 | C4 | direct (N × H) |
| 12. C42×Dic53 | C4 | semidirect |
| 13. C42×Dic53 | C4 | semidirect |
| 14. C42×Dic53 | C4 | semidirect |
| 15. C43×C53 | C4 | semidirect |
| 56. C42×C53 | C42 | semidirect |
| 63. C4×Dic53 | C42 | semidirect |
| 98. C4×C53 | #383 | semidirect |
| 101. Dic53 | #383 | semidirect |
| 120. C43 | #6157 | semidirect |
| 121. C53 | C4×#383 | semidirect |
| 169. C42 | C4×#6157 | semidirect |
| 206. C4 | #16811568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| #20289891 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| C43×D53 | 2 |
| C4×#383 | 53 |