Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 9. #16811489 | C4 | semidirect |
| 12. #16810378 | C4 | semidirect |
| 14. C53×#336 | C4 | semidirect |
| 20. C2×C4×#6157 | C8 | semidirect |
| 172. #336 | #6157 | semidirect |
| 173. C53 | #7017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290607 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| #20274782 | 2 |
| #7017 | 53 |