Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20272879 | C2 | direct (N × H) |
| 7. C2×#13133217 | C4 | semidirect |
| 10. #16810995 | C4 | semidirect |
| 13. C2×C4×#88322 | C4 | semidirect |
| 32. #13133217 | C2×C4 | semidirect |
| 38. C4×#88322 | C2×C4 | semidirect |
| 169. C2×C53 | #1409 | semidirect |
| 186. C53 | C2×#1409 | semidirect |
| 331. C2 | #20272879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810995 | 2 |
| C2×#16810416 | 2 |
| #20272879 | 2 |
| C2×C53×#353 | 2 |
| C2×#1409 | 53 |