Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
982 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 251 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×#16811003 | C2 | semidirect |
| 2. C2×#16810969 | C2 | semidirect |
| 3. #20274320 | C2 | direct (N × H) |
| 4. C2×C8×#88322 | C2 | semidirect |
| 9. #16811003 | C22 | semidirect |
| 11. #16810969 | C22 | semidirect |
| 14. C8×#88322 | C22 | semidirect |
| 104. C2×C53 | #1709 | semidirect |
| 121. C53 | C2×#1709 | semidirect |
| 200. C2 | #20274320 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811003 | 2 |
| C2×#16810969 | 2 |
| #20274320 | 2 |
| C2×C8×#88322 | 2 |
| C2×C53×#493 | 2 |
| C2×#1709 | 53 |