Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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. #20290512 | C2 | semidirect |
| 4. #20289931 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289607 | C2 | semidirect |
| 10. #16811657 | C4 | semidirect |
| 12. #16811651 | C4 | semidirect |
| 26. #16810369 | C4 | semidirect |
| 27. #16810366 | C4 | semidirect |
| 28. #16810366 | C4 | semidirect |
| 29. C53×#332 | C4 | semidirect |
| 204. #332 | #6157 | semidirect |
| 210. C53 | #8253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291440 | 2 |
| #20290512 | 2 |
| #20290096 | 2 |
| #20289931 | 2 |
| #20289612 | 2 |
| #20289607 | 2 |
| #20273363 | 2 |
| #8253 | 53 |