Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20273432 | C2 | semidirect |
| 5. #20272588 | C2 | semidirect |
| 6. #20272586 | C2 | semidirect |
| 7. C53×#1556 | C2 | semidirect |
| 149. #1556 | D53 | semidirect |
| 175. C53 | #9421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285172 | 2 |
| #20283785 | 2 |
| #20273432 | 2 |
| #20273349 | 2 |
| #20272588 | 2 |
| #20272586 | 2 |
| C53×#1556 | 2 |
| #9421 | 53 |