Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
830 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#16810360 | C2 | semidirect |
| 5. #20272986 | C2 | semidirect |
| 6. #20272557 | C2 | semidirect |
| 7. C2×C53×#451 | C2 | semidirect |
| 238. C2×#451 | D53 | semidirect |
| 277. C53 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810762 | 2 |
| #20280649 | 2 |
| C2×#16810360 | 2 |
| C2×#16810358 | 2 |
| #20272986 | 2 |
| #20272557 | 2 |
| C2×C53×#451 | 2 |
| #9965 | 53 |