Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. C2×#16810405 | C2 | semidirect |
| 3. #20272702 | C2 | semidirect |
| 4. #20272699 | C2 | semidirect |
| 5. C2×C53×H(3,ℤ/4) | C2 | semidirect |
| 6. C2×#13133239 | C4 | semidirect |
| 9. #16810881 | C4 | semidirect |
| 11. #16810876 | C4 | semidirect |
| 15. #16810661 | C4 | semidirect |
| 26. C2×Dic212 | C2×C4 | semidirect |
| 28. C2×D424 | C2×C4 | semidirect |
| 42. #13133149 | C2×C4 | semidirect |
| 43. #13133149 | C2×C4 | semidirect |
| 188. C2×H(3,ℤ/4) | D53 | semidirect |
| 215. C53 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284324 | 2 |
| C2×#16810405 | 2 |
| #20272702 | 2 |
| #20272699 | 2 |
| C2×C53×H(3,ℤ/4) | 2 |
| #11685 | 53 |