Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
256 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×#13095343 | C3 | semidirect |
| 3. C3×#13095342 | C3 | semidirect |
| 4. C3×(C19⋊C3)⋊C27 | C3 | semidirect |
| 5. #17987557 | C3 | semidirect |
| 6. #17987557 | C3 | semidirect |
| 7. #17987557 | C3 | semidirect |
| 8. C32⋊#10587020 | C3 | semidirect |
| 59. #10587020 | H(3,𝔽3) | semidirect |
| 81. C3×C19⋊C3 | C27⋊C3 | semidirect |
| 148. C19 | C27⋊H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095344 | 3 |
| C3×#13095343 | 3 |
| C3×#13095342 | 3 |
| C3×(C19⋊C3)⋊C27 | 3 |
| #17987557 | 3 |
| C32⋊#10587020 | 3 |
| #17987406 | 3 |
| C27⋊H(3,𝔽3) | 19 |