Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16810446 | C2 | semidirect |
| 5. #20272826 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#2155 | C2 | semidirect |
| 10. #16811039 | C4 | semidirect |
| 134. #2155 | D53 | semidirect |
| 161. C53 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| C2×#16810446 | 2 |
| #20274771 | 2 |
| #20274766 | 2 |
| #20272826 | 2 |
| #20272820 | 2 |
| C53×#2155 | 2 |
| #12833 | 53 |