Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
292 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C19 | H(3,𝔽3) |
| commutator | C32 | C32×C9×C19 |
| Frattini, cosocle | C33 | C33×C19 |
| socle | C32×C19 | C3×H(3,𝔽3) |
| prime radical | C3×C19×H(3,𝔽3) | C32 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C19 ◁ C32×C9×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C19×3−1+2 | C3 | semidirect |
| 4. C3×C92×C19 | C3 | semidirect |
| 5. C19×3−1+2⋊C9 | C3 | semidirect |
| 7. C19×#6867 | C3 | semidirect |
| 14. C19×#731 | C9 | direct (N × H) |
| 22. C9×#731 | C19 | direct (N × H) |
| 26. C19×3−1+2 | C3×C9 | semidirect |
| 38. C3×C9×C19 | C3×C9 | semidirect |
| 42. C9×3−1+2 | C3×C19 | semidirect |
| 44. C3×C92 | C3×C19 | semidirect |
| 45. 3−1+2⋊C9 | C3×C19 | semidirect |
| 47. #6867 | C3×C19 | semidirect |
| 62. C9×C19 | #731 | direct (N × H) |
| 69. #731 | C9×C19 | direct (N × H) |
| 86. 3−1+2 | C3×C9×C19 | semidirect |
| 98. C3×C9 | C3×C9×C19 | semidirect |
| 101. C19 | C9×#731 | direct (N × H) |
| 116. C9 | C19×#731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C19×#731 | 3 |
| C9×C19×3−1+2 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| C3×C92×C19 | 3 |
| C19×3−1+2⋊C9 | 3 |
| C19×H(3,𝔽3)⋊C9 | 3 |
| C19×#6867 | 3 |
| C9×#731 | 19 |