Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
872 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 315 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 |
|---|---|---|
| 2. #20273353 | C2 | semidirect |
| 3. #20273317 | C2 | semidirect |
| 4. #20273310 | C2 | semidirect |
| 119. C53 | #17692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283735 | 2 |
| #20273353 | 2 |
| #20273317 | 2 |
| #20273310 | 2 |
| C53×#3504 | 2 |
| #17692 | 53 |