Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 12. #16810399 | C4 | semidirect |
| 13. C4×#11719908 | C4 | semidirect |
| 126. C53 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276312 | 2 |
| #20274839 | 2 |
| #20272818 | 2 |
| #20272816 | 2 |
| #20272812 | 2 |
| #20272810 | 2 |
| C53×#1833 | 2 |
| #12893 | 53 |