Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2502 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 1. C2×#16811568 | C2 | semidirect |
| 2. #20289897 | C2 | semidirect |
| 8. C2×#13133214 | C4 | semidirect |
| 9. C2×#13133213 | C4 | semidirect |
| 12. C2×#127×C53 | C4 | semidirect |
| 48. C42×C53 | C22⋊C4 | semidirect |
| 49. C4×Dic53 | C22⋊C4 | semidirect |
| 95. C2×#127 | #6157 | semidirect |
| 100. C53 | #14661 | semidirect |
| 137. C42 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| #20289897 | 2 |
| C2×#127×D53 | 2 |
| #14661 | 53 |