Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1148 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 1. #20291561 | C2 | semidirect |
| 2. #20290203 | C2 | semidirect |
| 3. #20290176 | C2 | semidirect |
| 4. #20290169 | C2 | semidirect |
| 8. #16811644 | C22 | semidirect |
| 9. C4×#11719940 | C22 | semidirect |
| 10. #16811479 | C22 | semidirect |
| 11. #16811479 | C22 | semidirect |
| 12. #16811478 | C22 | semidirect |
| 13. #16811478 | C22 | semidirect |
| 166. C53 | #17688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291561 | 2 |
| #20290203 | 2 |
| #20290176 | 2 |
| #20290169 | 2 |
| #20288509 | 2 |
| #17688 | 53 |