Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283841 | C2 | semidirect |
| 3. C4×#13133145 | C2 | semidirect |
| 4. #20273132 | C2 | semidirect |
| 5. #20272604 | C2 | semidirect |
| 6. #20272548 | C2 | semidirect |
| 7. C53×#1962 | C2 | semidirect |
| 10. #16810915 | C4 | semidirect |
| 11. #16810910 | C4 | semidirect |
| 12. #16810820 | C4 | semidirect |
| 13. #16810815 | C4 | semidirect |
| 172. D212 | #104 | semidirect |
| 213. #1962 | D53 | semidirect |
| 249. C53 | #8969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284769 | 2 |
| #20283841 | 2 |
| C4×#13133145 | 2 |
| #20273132 | 2 |
| #20272604 | 2 |
| #20272548 | 2 |
| C53×#1962 | 2 |
| #8969 | 53 |