Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 476 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. #20275691 | C2 | semidirect |
| 5. #20273137 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1299 | C2 | semidirect |
| 11. #16810909 | C4 | semidirect |
| 12. #16810904 | C4 | semidirect |
| 13. #16810834 | C4 | semidirect |
| 14. #16810829 | C4 | semidirect |
| 206. #1299 | D53 | semidirect |
| 238. C53 | #8972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284787 | 2 |
| #20283845 | 2 |
| #20275691 | 2 |
| C4×#13133143 | 2 |
| #20273137 | 2 |
| #20272547 | 2 |
| C53×#1299 | 2 |
| #8972 | 53 |