Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 203 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. #20276958 | C2 | direct (N × H) |
| 3. C2×#16810423 | C2 | semidirect |
| 4. C2×#16810399 | C2 | semidirect |
| 5. C2×C53×#499 | C2 | semidirect |
| 12. #16810423 | C22 | semidirect |
| 13. #16810399 | C22 | semidirect |
| 16. C53×#499 | C22 | semidirect |
| 98. C2×#499 | D53 | semidirect |
| 103. C2×C53 | #2244 | semidirect |
| 113. #499 | C2×D53 | semidirect |
| 121. C53 | C2×#2244 | semidirect |
| 200. C2 | #20276958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| #20276958 | 2 |
| C2×#16810423 | 2 |
| C2×#16810399 | 2 |
| C2×C53×#499 | 2 |
| C2×#2244 | 53 |