Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 14. #16810398 | C4 | semidirect |
| 15. C4×#11719908 | C4 | semidirect |
| 16. C4×C16×C53 | C4 | semidirect |
| 56. C16×C53 | C4⋊C4 | semidirect |
| 57. #11719908 | C4⋊C4 | semidirect |
| 81. C4×C53 | #365 | semidirect |
| 106. C4×C16 | #6157 | semidirect |
| 107. C53 | #12903 | semidirect |
| 148. C16 | C4⋊#6157 | semidirect |
| 174. C4 | #16811548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811548 | 2 |
| #20290654 | 2 |
| #20290650 | 2 |
| C4×#13133156 | 2 |
| #12903 | 53 |