Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16810435 | C2 | semidirect |
| 3. C2×#16810405 | C2 | semidirect |
| 4. #20272815 | C2 | semidirect |
| 5. C2×C53×#430 | C2 | semidirect |
| 50. #108×C53 | D4 | semidirect |
| 145. C2×#430 | D53 | semidirect |
| 169. C53 | #13010 | semidirect |
| 197. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810876 | 2 |
| C2×#16810435 | 2 |
| C2×#16810405 | 2 |
| #20272815 | 2 |
| C2×C53×#430 | 2 |
| #13010 | 53 |