Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. C2×#16810420 | C2 | semidirect |
| 2. #20273339 | C2 | semidirect |
| 3. #20272863 | C2 | semidirect |
| 8. #16810420 | C22 | semidirect |
| 10. #16810363 | C22 | semidirect |
| 197. C53 | #13565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810420 | 2 |
| #20273339 | 2 |
| #20272863 | 2 |
| C2×C53×#455 | 2 |
| #13565 | 53 |