Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1042 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 256 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. #20290254 | C2 | direct (N × H) |
| 3. C2×#16811482 | C2 | semidirect |
| 10. #16811482 | C22 | semidirect |
| 148. C2×C53 | #1561 | semidirect |
| 167. C53 | C2×#1561 | semidirect |
| 290. C2 | #20290254 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811626 | 2 |
| #20290254 | 2 |
| C2×#16811482 | 2 |
| C2×#16811176 | 2 |
| C2×#1561 | 53 |