Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1422 conjugacy classes of subgroups; only the 336 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 336 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. #16810469 | C4 | semidirect |
| 13. #16810469 | C4 | semidirect |
| 14. #16810468 | C4 | semidirect |
| 16. C53×#376 | C4 | semidirect |
| 127. #376 | #6157 | semidirect |
| 131. C53 | #13854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊#6157 | 2 |
| #20289901 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| #376×D53 | 2 |
| #13854 | 53 |