Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 4. C2×D53⋊C16 | C4 | semidirect |
| 9. #16811497 | C4 | semidirect |
| 13. #16810386 | C4 | semidirect |
| 14. C53×#340 | C4 | semidirect |
| 150. #340 | #6157 | semidirect |
| 151. C53 | #7230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290592 | 2 |
| #20274743 | 2 |
| #7230 | 53 |