Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
218 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C19 |
| prime radical | C19×#6856 | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ C32×C9×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#6894 | C3 | semidirect |
| 2. C19×#6893 | C3 | semidirect |
| 3. C9×C19×3−1+2 | C3 | semidirect |
| 4. C9×C19×H(3,𝔽3) | C3 | semidirect |
| 5. C19×#6860 | C3 | semidirect |
| 6. C19×#6860 | C3 | semidirect |
| 7. C19×#6859 | C3 | semidirect |
| 8. C19×#6858 | C3 | semidirect |
| 9. C19×#6858 | C3 | semidirect |
| 10. C19×#6857 | C3 | semidirect |
| 11. C19×#6857 | C3 | semidirect |
| 12. C19×#6857 | C3 | semidirect |
| 39. #10624623 | C19 | direct (N × H) |
| 64. #6894 | C3×C19 | semidirect |
| 65. #6893 | C3×C19 | semidirect |
| 66. C9×3−1+2 | C3×C19 | semidirect |
| 67. C9×H(3,𝔽3) | C3×C19 | semidirect |
| 68. #6860 | C3×C19 | semidirect |
| 69. #6860 | C3×C19 | semidirect |
| 70. #6859 | C3×C19 | semidirect |
| 71. #6858 | C3×C19 | semidirect |
| 72. #6858 | C3×C19 | semidirect |
| 73. #6857 | C3×C19 | semidirect |
| 74. #6857 | C3×C19 | semidirect |
| 75. #6857 | C3×C19 | semidirect |
| 159. C19 | #10624623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#6894 | 3 |
| C19×#6893 | 3 |
| C9×C19×3−1+2 | 3 |
| C9×C19×H(3,𝔽3) | 3 |
| C19×#6860 | 3 |
| C19×#6859 | 3 |
| C19×#6858 | 3 |
| C19×#6857 | 3 |
| C19×#6856 | 3 |
| #10624623 | 19 |