Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20274568 | C2 | semidirect |
| 3. C2×#16810370 | C2 | semidirect |
| 5. C53×#1831 | C2 | semidirect |
| 132. #1831 | D53 | semidirect |
| 156. C53 | #9710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283072 | 2 |
| #20274568 | 2 |
| C2×#16810370 | 2 |
| C2×#16810366 | 2 |
| C53×#1831 | 2 |
| #9710 | 53 |