Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20283591 | C2 | semidirect |
| 3. C2×#16810425 | C2 | semidirect |
| 4. #20275623 | C2 | semidirect |
| 5. #20272825 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C2×C53×#359 | C2 | semidirect |
| 11. #16811058 | C4 | semidirect |
| 34. C2×D424 | C2×C4 | semidirect |
| 46. #13133157 | C2×C4 | semidirect |
| 184. C2×#359 | D53 | semidirect |
| 216. C53 | #13022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| #20283591 | 2 |
| C2×#16810425 | 2 |
| #20275623 | 2 |
| #20272825 | 2 |
| #20272803 | 2 |
| C2×C53×#359 | 2 |
| #13022 | 53 |