Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20275695 | C2 | semidirect |
| 4. #20273280 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 10. #16810995 | C4 | semidirect |
| 11. #16810969 | C4 | semidirect |
| 29. #13133217 | C2×C4 | semidirect |
| 30. #13133217 | C2×C4 | semidirect |
| 48. C4×#88322 | C2×C4 | semidirect |
| 116. C4×Dic53 | SD16 | semidirect |
| 221. C53 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285656 | 2 |
| #20277441 | 2 |
| #20275695 | 2 |
| #20273280 | 2 |
| #20272575 | 2 |
| #20272543 | 2 |
| C53×#1545 | 2 |
| #9295 | 53 |