Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20290668 | C2 | semidirect |
| 4. #20290667 | C2 | semidirect |
| 5. #20289598 | C2 | semidirect |
| 6. #20289598 | C2 | semidirect |
| 142. C22×D53 | #108 | semidirect |
| 245. C53 | #8859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291570 | 2 |
| #20290695 | 2 |
| #20290668 | 2 |
| #20290667 | 2 |
| #20289598 | 2 |
| #20273032 | 2 |
| #8859 | 53 |