Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#16810440 | C2 | semidirect |
| 5. #20276436 | C2 | semidirect |
| 6. #20274839 | C2 | semidirect |
| 7. C53×#2110 | C2 | semidirect |
| 13. #16811007 | C4 | semidirect |
| 14. #16811003 | C4 | semidirect |
| 169. #2110 | D53 | semidirect |
| 195. C53 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285209 | 2 |
| C2×#16810440 | 2 |
| #20276452 | 2 |
| #20276444 | 2 |
| #20276436 | 2 |
| #20274839 | 2 |
| C53×#2110 | 2 |
| #13216 | 53 |