Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 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×#16811000 | C2 | semidirect |
| 2. C2×#16810999 | C2 | semidirect |
| 3. C2×#16810971 | C2 | semidirect |
| 4. #20274379 | C2 | direct (N × H) |
| 5. C2×#16810344 | C2 | semidirect |
| 6. C2×C53×#492 | C2 | semidirect |
| 11. #16811000 | C22 | semidirect |
| 13. #16810999 | C22 | semidirect |
| 15. #16810971 | C22 | semidirect |
| 18. #16810344 | C22 | semidirect |
| 23. C53×#492 | C22 | semidirect |
| 80. C2×C8×C53 | D8 | semidirect |
| 119. C8×C53 | C2×D8 | semidirect |
| 139. C2×#492 | D53 | semidirect |
| 144. C2×C53 | #1721 | semidirect |
| 159. #492 | C2×D53 | semidirect |
| 166. C53 | C2×#1721 | semidirect |
| 226. C2×C8 | #11719922 | semidirect |
| 262. C8 | C2×#11719922 | semidirect |
| 280. C2 | #20274379 | 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 |
| C2×#16810999 | 2 |
| C2×#16810971 | 2 |
| #20274379 | 2 |
| C2×#16810344 | 2 |
| C2×C53×#492 | 2 |
| C2×#1721 | 53 |