Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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×#16810491 | C2 | semidirect |
| 4. #20272948 | C2 | semidirect |
| 5. C2×C43×C53 | C2 | semidirect |
| 8. C2×#13133211 | C4 | semidirect |
| 58. C42×C53 | C22⋊C4 | semidirect |
| 78. C2×C4×C53 | #126 | semidirect |
| 103. C2×C43 | D53 | semidirect |
| 123. C53 | #14711 | semidirect |
| 167. C42 | #11719921 | semidirect |
| 191. C2×C4 | #13133211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133211 | 2 |
| C2×#16810491 | 2 |
| #20272953 | 2 |
| #20272948 | 2 |
| C2×C43×C53 | 2 |
| #14711 | 53 |