Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3294 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20282979 | C2 | direct (N × H) |
| 2. C2×#16810559 | C2 | semidirect |
| 3. C2×#16810546 | C2 | semidirect |
| 6. C22×C4⋊Dic53 | C22 | semidirect |
| 7. C22×#11719919 | C22 | semidirect |
| 11. #16810559 | C22 | semidirect |
| 12. #16810546 | C22 | semidirect |
| 14. C2×#13133124 | C22 | semidirect |
| 21. C2×C4⋊Dic53 | C23 | semidirect |
| 23. C2×#11719919 | C23 | semidirect |
| 30. #13133124 | C23 | semidirect |
| 127. C2×C53 | #2842 | semidirect |
| 144. C53 | C2×#2842 | semidirect |
| 247. C2 | #20282979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282979 | 2 |
| C2×#16810559 | 2 |
| C2×#16810546 | 2 |
| C2×#16810479 | 2 |
| C2×C53×#379 | 2 |
| C2×#2842 | 53 |