Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
560 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #16811489 | C4 | semidirect |
| 11. C2×C4⋊#88322 | C4 | semidirect |
| 14. C2×C4⋊C8×C53 | C4 | semidirect |
| 28. (C2×#6157)⋊C4 | C8 | semidirect |
| 190. C2×C4⋊C8 | #6157 | semidirect |
| 198. C53 | #7028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133274 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| #20274692 | 2 |
| #7028 | 53 |