Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3998 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 3998 conjugacy classes of subgroups — too many to draw. Only its 416 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. #20289905 | C2 | semidirect |
| 7. C23×Dic106 | C4 | semidirect |
| 9. C22×Q8×D53 | C4 | semidirect |
| 12. C23×Q8×C53 | C4 | semidirect |
| 103. C23×Q8 | #6157 | semidirect |
| 108. C53 | #14336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811566 | 2 |
| #20289905 | 2 |
| C23×Q8×D53 | 2 |
| #14336 | 53 |