Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 7. #16810418 | C4 | semidirect |
| 9. #16810363 | C4 | semidirect |
| 11. C53×#519 | C4 | semidirect |
| 13. C2×#101×C53 | C4 | semidirect |
| 127. #519 | Dic53 | semidirect |
| 129. C2×#101 | Dic53 | semidirect |
| 137. C53 | #7489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810418 | 2 |
| C2×#16810363 | 2 |
| C53×#1888 | 2 |
| #7489 | 53 |