Finite Group DatabasebetaFinite Group Databasebeta← (C3×#4296)⋊H(3,𝔽3) #28356860
Order 13851.
842 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 117 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. C33×#4296 | C3 | semidirect |
| 2. C3×C32⋊#4296 | C3 | semidirect |
| 3. C3×C32⋊#4296 | C3 | semidirect |
| 13. C3×C32⋊(C19⋊C3) | C9 | semidirect |
| 14. C3×C32⋊(C19⋊C3) | C9 | semidirect |
| 17. C3×C19×H(3,𝔽3) | C9 | semidirect |
| 20. C33×C19 | C3×C9 | semidirect |
| 28. C32×C19⋊C3 | C3×C9 | semidirect |
| 37. C3×#4296 | H(3,𝔽3) | semidirect |
| 48. C32×C19 | C32⋊C9 | semidirect |
| 59. C3×C19⋊C3 | C32⋊C9 | semidirect |
| 72. C3×H(3,𝔽3) | #4296 | semidirect |
| 100. C33 | C3×#4296 | semidirect |
| 110. C19 | #10624555 | semidirect |
| 128. C32 | C32⋊#4296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#4296 | 3 |
| C3×C32⋊#4296 | 3 |
| C3×H(3,𝔽3)×C19⋊C3 | 3 |
| #10624555 | 19 |