Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×#13095322 | C3 | semidirect |
| 3. C3×#13095307 | C3 | semidirect |
| 4. #17987388 | C3 | direct (N × H) |
| 5. C3×C19×#733 | C3 | semidirect |
| 10. #13095322 | C32 | semidirect |
| 14. #13095307 | C32 | semidirect |
| 18. C19×#733 | C32 | semidirect |
| 37. C3×#733 | C19⋊C3 | semidirect |
| 60. #733 | C3×C19⋊C3 | semidirect |
| 67. C3×C19 | #6883 | semidirect |
| 86. C19 | C3×#6883 | semidirect |
| 101. C3 | #17987388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095322 | 3 |
| C3×#13095320 | 3 |
| C3×#13095307 | 3 |
| #17987388 | 3 |
| C3×C19×#733 | 3 |
| C3×#6883 | 19 |