Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
994 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 994 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. #20290220 | C2 | direct (N × H) |
| 3. C2×#16811482 | C2 | semidirect |
| 10. #16811482 | C22 | semidirect |
| 140. C2×C53 | #1544 | semidirect |
| 159. C53 | C2×#1544 | semidirect |
| 274. C2 | #20290220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811640 | 2 |
| #20290220 | 2 |
| C2×#16811482 | 2 |
| C2×#16811176 | 2 |
| C2×#1544 | 53 |