Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
582 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 203 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. #20276962 | C2 | direct (N × H) |
| 98. C2×C53 | #2245 | semidirect |
| 115. C53 | C2×#2245 | semidirect |
| 188. C2 | #20276962 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811003 | 2 |
| #20276962 | 2 |
| C2×#16810426 | 2 |
| C2×#16810399 | 2 |
| C2×C53×#499 | 2 |
| C2×#2245 | 53 |