Finite Group DatabasebetaFinite Group Databasebeta← C3×(C3×C19⋊C3)⋊H(3,𝔽3) #28355938
Order 13851.
3824 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 3824 conjugacy classes of subgroups — too many to draw. Only its 382 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. C34×C19⋊C3 | C3 | semidirect |
| 2. C32×C32⋊(C19⋊C3) | C3 | semidirect |
| 3. C32×C32⋊(C19⋊C3) | C3 | semidirect |
| 4. (C3×C19⋊C3)⋊H(3,𝔽3) | C3 | direct (N × H) |
| 5. C32×C19×H(3,𝔽3) | C3 | semidirect |
| 9. C33×C19⋊C3 | C32 | semidirect |
| 10. C33×C19⋊C3 | C32 | semidirect |
| 13. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 14. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 16. C34×C19 | C32 | semidirect |
| 18. C3×C19×H(3,𝔽3) | C32 | semidirect |
| 23. C33×C19 | H(3,𝔽3) | semidirect |
| 26. C33×C19 | C33 | semidirect |
| 34. C32×C19⋊C3 | H(3,𝔽3) | semidirect |
| 36. C32×C19⋊C3 | C33 | semidirect |
| 43. C32×H(3,𝔽3) | C19⋊C3 | semidirect |
| 52. C32×C19 | C3×H(3,𝔽3) | semidirect |
| 61. C3×C19⋊C3 | C3×H(3,𝔽3) | semidirect |
| 68. C34 | C3×C19⋊C3 | semidirect |
| 74. C3×H(3,𝔽3) | C3×C19⋊C3 | semidirect |
| 77. C3×C19 | C32⋊H(3,𝔽3) | semidirect |
| 95. C33 | C32⋊(C19⋊C3) | semidirect |
| 98. C33 | C32×C19⋊C3 | semidirect |
| 102. C19 | C3×C32⋊H(3,𝔽3) | semidirect |
| 118. C32 | C3×C32⋊(C19⋊C3) | semidirect |
| 124. C3 | (C3×C19⋊C3)⋊H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C19⋊C3 | 3 |
| C32×C32⋊(C19⋊C3) | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C32×C19×H(3,𝔽3) | 3 |
| C3×C32⋊H(3,𝔽3) | 19 |