Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. C2×C4×#11719908 | C2 | semidirect |
| 4. #20272812 | C2 | semidirect |
| 5. C4×#108×C53 | C2 | semidirect |
| 14. #16810429 | C4 | direct (N × H) |
| 34. C2×#11719908 | C2×C4 | semidirect |
| 44. #108×C53 | C2×C4 | semidirect |
| 112. C4×C53 | #359 | semidirect |
| 121. C4×#108 | D53 | semidirect |
| 141. C53 | C4×#359 | semidirect |
| 162. #108 | C4×D53 | semidirect |
| 235. C4 | #16810429 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133239 | 2 |
| C2×#16810429 | 2 |
| C2×C4×#11719908 | 2 |
| #20272812 | 2 |
| C4×#108×C53 | 2 |
| C4×#359 | 53 |