Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
328 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 88 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. C9×C32⋊(C19⋊C3) | C3 | semidirect |
| 3. C3×C9×#4294 | C3 | semidirect |
| 4. H(3,𝔽3)⋊#4294 | C3 | semidirect |
| 5. #17987342 | C3 | semidirect |
| 6. #17987338 | C3 | semidirect |
| 7. C9×C19×H(3,𝔽3) | C3 | semidirect |
| 12. #13095319 | C9 | direct (N × H) |
| 27. C19×H(3,𝔽3) | C3×C9 | semidirect |
| 34. C32⋊(C19⋊C3) | C3×C9 | semidirect |
| 40. C3×#4294 | C3×C9 | semidirect |
| 44. C9×H(3,𝔽3) | C19⋊C3 | semidirect |
| 62. C9×C19 | #732 | semidirect |
| 93. H(3,𝔽3) | C9×C19⋊C3 | semidirect |
| 106. C19 | C9×#732 | semidirect |
| 123. C9 | #13095319 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095319 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| C3×C9×#4294 | 3 |
| H(3,𝔽3)⋊#4294 | 3 |
| #17987342 | 3 |
| #17987338 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| C9×#732 | 19 |