Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
724 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#16810779 | C2 | semidirect |
| 4. #20273080 | C2 | semidirect |
| 6. #20272602 | C2 | semidirect |
| 7. C53×#1784 | C2 | semidirect |
| 212. #1784 | D53 | semidirect |
| 246. C53 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285522 | 2 |
| C2×#16810779 | 2 |
| C2×#16810762 | 2 |
| #20273080 | 2 |
| #20273076 | 2 |
| #20272602 | 2 |
| C53×#1784 | 2 |
| #9989 | 53 |