Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
830 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 111 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×#16810779 | C2 | semidirect |
| 4. C2×#16810359 | C2 | semidirect |
| 6. #20272558 | C2 | semidirect |
| 7. C53×#1446 | C2 | semidirect |
| 243. #1446 | 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×#16810779 | 2 |
| C2×#16810762 | 2 |
| #20280643 | 2 |
| C2×#16810359 | 2 |
| C2×#16810356 | 2 |
| #20272558 | 2 |
| C53×#1446 | 2 |
| #9965 | 53 |