Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1092 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#16811373 | C2 | semidirect |
| 2. C2×#16810806 | C2 | semidirect |
| 3. #20276735 | C2 | direct (N × H) |
| 4. C2×#16810421 | C2 | semidirect |
| 5. C2×#16810420 | C2 | semidirect |
| 10. #16811373 | C22 | semidirect |
| 17. #16810806 | C22 | semidirect |
| 20. #16810421 | C22 | semidirect |
| 21. #16810420 | C22 | semidirect |
| 225. C2×C53 | #2203 | semidirect |
| 249. C53 | C2×#2203 | semidirect |
| 439. C2 | #20276735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811373 | 2 |
| C2×#16810806 | 2 |
| #20276735 | 2 |
| C2×#16810421 | 2 |
| C2×#16810420 | 2 |
| C2×C53×#454 | 2 |
| C2×#2203 | 53 |