Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#13133163 | C2 | semidirect |
| 4. #20276984 | C2 | direct (N × H) |
| 5. C2×#16810399 | C2 | semidirect |
| 6. C2×C53×#494 | C2 | semidirect |
| 12. C2×#13133163 | C22 | semidirect |
| 18. #16810399 | C22 | semidirect |
| 23. C53×#494 | C22 | semidirect |
| 135. C2×#494 | D53 | semidirect |
| 138. C2×C53 | #2251 | semidirect |
| 157. #494 | C2×D53 | semidirect |
| 160. C53 | C2×#2251 | semidirect |
| 268. C2 | #20276984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133163 | 2 |
| C22×#13133160 | 2 |
| C2×#16811007 | 2 |
| #20276984 | 2 |
| C2×#16810399 | 2 |
| C2×C53×#494 | 2 |
| C2×#2251 | 53 |