Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
798 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 4. #20274349 | C2 | direct (N × H) |
| 122. C2×C53 | #1716 | semidirect |
| 143. C53 | C2×#1716 | semidirect |
| 234. C2 | #20274349 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811019 | 2 |
| C2×#16811003 | 2 |
| C2×#16810973 | 2 |
| #20274349 | 2 |
| C2×#16810344 | 2 |
| C2×C53×#498 | 2 |
| C2×#1716 | 53 |