Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 9. #16810399 | C4 | semidirect |
| 10. C4×#11719908 | C4 | semidirect |
| 16. C53×#347 | C4 | semidirect |
| 88. #347 | Dic53 | semidirect |
| 94. C53 | #12597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276312 | 2 |
| #20274470 | 2 |
| #20272805 | 2 |
| #20272802 | 2 |
| C53×#2110 | 2 |
| #12597 | 53 |