Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1510 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1510 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 6. #16811566 | C4 | semidirect |
| 12. C22×#11719919 | C4 | semidirect |
| 14. C22×C4×Dic53 | C4 | semidirect |
| 15. C22×C42×C53 | C4 | semidirect |
| 175. C22×C42 | #6157 | semidirect |
| 180. C53 | #10726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811566 | 2 |
| C2×#16811501 | 2 |
| C22×#13133174 | 2 |
| #10726 | 53 |