Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
304 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 69 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. H(3,𝔽3)×#4296 | C3 | semidirect |
| 2. C3×#13095339 | C3 | semidirect |
| 3. H(3,𝔽3)⋊#4296 | C3 | semidirect |
| 4. #17987560 | C3 | semidirect |
| 14. #13095320 | C9 | semidirect |
| 15. #13095319 | C9 | semidirect |
| 16. C19×#732 | C9 | semidirect |
| 26. C19×H(3,𝔽3) | C3×C9 | semidirect |
| 27. C3×C9×C19 | C3×C9 | semidirect |
| 29. C32⋊(C19⋊C3) | C3×C9 | semidirect |
| 30. C3×#4294 | C3×C9 | semidirect |
| 59. #732 | #4296 | semidirect |
| 74. H(3,𝔽3) | C3×#4296 | semidirect |
| 84. C3×C9 | C3×#4296 | semidirect |
| 85. C19 | #10624722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#4296 | 3 |
| C3×#13095339 | 3 |
| H(3,𝔽3)⋊#4296 | 3 |
| #17987560 | 3 |
| C19⋊C3×#732 | 3 |
| #10624722 | 19 |