Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 5. #16810416 | C4 | semidirect |
| 8. C2×#97×C53 | C4 | semidirect |
| 9. C53×#382 | C4 | semidirect |
| 100. C2×#97 | Dic53 | semidirect |
| 101. #382 | Dic53 | semidirect |
| 104. C53 | #7504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| C53×#1961 | 2 |
| #7504 | 53 |