Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 10. #16811509 | C4 | semidirect |
| 11. C4×#11719910 | C4 | semidirect |
| 14. #16810399 | C4 | semidirect |
| 15. #16810398 | C4 | semidirect |
| 16. C53×#346 | C4 | semidirect |
| 96. #346 | #6157 | semidirect |
| 99. C53 | #12592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D53⋊C16 | 2 |
| #20290371 | 2 |
| (C2×#6157)⋊C16 | 2 |
| #346×D53 | 2 |
| #12592 | 53 |