Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20273317 | C2 | semidirect |
| 5. #20272579 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#2336 | C2 | semidirect |
| 9. #16811033 | C4 | semidirect |
| 10. #16810989 | C4 | semidirect |
| 193. #2336 | D53 | semidirect |
| 228. C53 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285905 | 2 |
| #20275633 | 2 |
| #20273317 | 2 |
| #20273261 | 2 |
| #20272579 | 2 |
| #20272571 | 2 |
| C53×#2336 | 2 |
| #9382 | 53 |