Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 12. #16811512 | C4 | semidirect |
| 13. C4×#11719910 | C4 | semidirect |
| 17. C4⋊#11719908 | C4 | semidirect |
| 18. #16810441 | C4 | semidirect |
| 19. C53×C4⋊C16 | C4 | semidirect |
| 70. #11719910 | C4⋊C4 | semidirect |
| 104. C4×C53 | #347 | semidirect |
| 130. C4⋊C16 | #6157 | semidirect |
| 135. C53 | #12666 | semidirect |
| 223. C4 | #16811513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811513 | 2 |
| C4×#13133292 | 2 |
| #20290509 | 2 |
| #20289755 | 2 |
| #20276469 | 2 |
| #12666 | 53 |