Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#16810437 | C2 | semidirect |
| 3. #20276432 | C2 | semidirect |
| 4. #20274594 | C2 | semidirect |
| 5. C2×C53×#364 | C2 | semidirect |
| 10. #16811000 | C4 | semidirect |
| 37. #13133153 | D4 | semidirect |
| 38. #13133151 | D4 | semidirect |
| 128. C2×#364 | D53 | semidirect |
| 151. C53 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810437 | 2 |
| #20276432 | 2 |
| #20274594 | 2 |
| C2×C53×#364 | 2 |
| #13261 | 53 |