Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16811029 | C2 | semidirect |
| 3. #20274024 | C2 | direct (N × H) |
| 4. C2×#16810364 | C2 | semidirect |
| 16. #16811029 | C22 | semidirect |
| 20. #16810364 | C22 | semidirect |
| 172. C2×C53 | #1660 | semidirect |
| 197. C53 | C2×#1660 | semidirect |
| 334. C2 | #20274024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811373 | 2 |
| C2×#16811029 | 2 |
| #20274024 | 2 |
| C2×#16810364 | 2 |
| C2×#16810363 | 2 |
| C2×C53×#497 | 2 |
| C2×#1660 | 53 |