Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2598 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2598 conjugacy classes of subgroups — too many to draw. Only its 987 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. #95×Dic53 | C2 | semidirect |
| 6. C4×C22⋊Dic53 | C4 | semidirect |
| 9. C2×#95×C53 | C4 | semidirect |
| 14. C2×C4×Dic53 | C2×C4 | semidirect |
| 15. #13133124 | C2×C4 | semidirect |
| 30. C22×C4×C53 | C42 | semidirect |
| 37. C22⋊Dic53 | C42 | semidirect |
| 83. C2×#95 | Dic53 | semidirect |
| 85. C53 | #13749 | semidirect |
| 108. C22×C4 | C4×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊Dic53 | 2 |
| #95×Dic53 | 2 |
| C22×#95×C53 | 2 |
| #13749 | 53 |