Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #20291235 | C2 | semidirect |
| 4. #20290018 | C2 | semidirect |
| 5. #20289611 | C2 | semidirect |
| 6. #20289570 | C2 | semidirect |
| 27. #16810834 | C4 | semidirect |
| 28. #16810833 | C4 | semidirect |
| 29. #16810820 | C4 | semidirect |
| 32. C53×#460 | C4 | semidirect |
| 240. #460 | #6157 | semidirect |
| 257. C53 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291235 | 2 |
| #20290144 | 2 |
| #20290095 | 2 |
| #20290018 | 2 |
| #20289611 | 2 |
| #20289570 | 2 |
| #20284182 | 2 |
| #9182 | 53 |