Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #20272921 | C2 | direct (N × H) |
| 12. C53×M64 | C4 | semidirect |
| 14. C2×C32×C53 | C4 | semidirect |
| 28. C32×C53 | C2×C4 | semidirect |
| 76. C2×C53 | #1426 | semidirect |
| 81. M64 | Dic53 | semidirect |
| 83. C2×C32 | Dic53 | semidirect |
| 88. C53 | C2×#1426 | semidirect |
| 102. C32 | C2×Dic53 | semidirect |
| 145. C2 | #20272921 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810453 | 2 |
| C2×#16810451 | 2 |
| #20272921 | 2 |
| C2×C53×M64 | 2 |
| C2×#1426 | 53 |