Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic848 | C2 | semidirect |
| 3. #20272931 | C2 | direct (N × H) |
| 4. C2×C53×C64 | C2 | semidirect |
| 8. Dic848 | C22 | semidirect |
| 12. C53×C64 | C22 | semidirect |
| 50. C2×C64 | D53 | semidirect |
| 51. C2×C53 | SD128 | semidirect |
| 61. C64 | C2×D53 | semidirect |
| 62. C53 | C2×SD128 | semidirect |
| 97. C2 | #20272931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic848 | 2 |
| C2×D1696 | 2 |
| #20272931 | 2 |
| C2×C53×C64 | 2 |
| C2×SD128 | 53 |