Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
188 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C19 | #6911 |
| commutator, Frattini, cosocle | C3×C9 | C33×C19 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C19 ◁ C32×C19 ◁ C3×C19×3−1+2 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#6913 | C3 | semidirect |
| 2. C19×#6912 | C3 | semidirect |
| 3. C19×#6900 | C3 | semidirect |
| 4. C19×#6883 | C3 | semidirect |
| 5. C19×#6882 | C3 | semidirect |
| 6. C19×#6882 | C3 | semidirect |
| 7. C19×#6881 | C3 | semidirect |
| 8. C19×#6880 | C3 | semidirect |
| 9. C19×#6878 | C3 | semidirect |
| 26. #10624852 | C19 | direct (N × H) |
| 44. #6913 | C3×C19 | semidirect |
| 45. #6912 | C3×C19 | semidirect |
| 46. #6900 | C3×C19 | semidirect |
| 47. #6883 | C3×C19 | semidirect |
| 48. #6882 | C3×C19 | semidirect |
| 49. #6882 | C3×C19 | semidirect |
| 50. #6881 | C3×C19 | semidirect |
| 51. #6880 | C3×C19 | semidirect |
| 52. #6878 | C3×C19 | semidirect |
| 103. C19 | #10624852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#6913 | 3 |
| C19×#6912 | 3 |
| C19×#6900 | 3 |
| C19×#6883 | 3 |
| C19×#6882 | 3 |
| C19×#6881 | 3 |
| C19×#6880 | 3 |
| C19×#6878 | 3 |
| #10624852 | 19 |