Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20272896 | C2 | direct (N × H) |
| 13. C2×Q32×C53 | C4 | semidirect |
| 28. Q32×C53 | C2×C4 | semidirect |
| 81. C2×C53 | #1416 | semidirect |
| 88. C2×Q32 | Dic53 | semidirect |
| 96. C53 | C2×#1416 | semidirect |
| 106. Q32 | C2×Dic53 | semidirect |
| 157. C2 | #20272896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133123 | 2 |
| C2×#16810449 | 2 |
| #20272896 | 2 |
| C22×Q32×C53 | 2 |
| C2×#1416 | 53 |