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 |
|---|---|---|
| 1. C2×#16810491 | C2 | semidirect |
| 2. C2×C42×Dic53 | C2 | semidirect |
| 4. #20272947 | C2 | semidirect |
| 14. C2×#126×C53 | C4 | semidirect |
| 59. C42×C53 | C22⋊C4 | semidirect |
| 85. C2×Dic53 | #126 | semidirect |
| 113. C2×#126 | Dic53 | semidirect |
| 123. C53 | #14711 | semidirect |
| 167. C42 | C22⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| C2×C42×Dic53 | 2 |
| #20272952 | 2 |
| #20272947 | 2 |
| C22×#126×C53 | 2 |
| #14711 | 53 |