Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
428 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×#13095344 | C3 | semidirect |
| 2. #17987557 | C3 | semidirect |
| 3. C32⋊#10587020 | C3 | semidirect |
| 6. C3×#10587020 | C32 | semidirect |
| 49. C32×C19 | C27⋊C3 | semidirect |
| 58. C3×C19⋊C3 | C27⋊C3 | semidirect |
| 109. C19 | #10624683 | semidirect |
| 120. C32 | #13095344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095344 | 3 |
| #17987557 | 3 |
| C32⋊#10587020 | 3 |
| C32×C9×C19⋊C3 | 3 |
| #10624683 | 19 |