Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20276489 | C2 | semidirect |
| 5. #20272829 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#1953 | C2 | semidirect |
| 18. #16810435 | C4 | semidirect |
| 38. #13133157 | C2×C4 | semidirect |
| 53. #108×C53 | C2×C4 | semidirect |
| 137. #1953 | D53 | semidirect |
| 161. C53 | #12953 | semidirect |
| 188. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283568 | 2 |
| #20276489 | 2 |
| C2×#16810435 | 2 |
| #20272829 | 2 |
| #20272801 | 2 |
| C53×#1953 | 2 |
| #12953 | 53 |