Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 286 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 |
|---|---|---|
| 2. #17987468 | C3 | semidirect |
| 3. #17987460 | C3 | semidirect |
| 4. #17987447 | C3 | semidirect |
| 5. #17987446 | C3 | semidirect |
| 6. #17987441 | C3 | semidirect |
| 7. #17987440 | C3 | semidirect |
| 8. #17987439 | C3 | semidirect |
| 9. #17987438 | C3 | semidirect |
| 11. #17987415 | C3 | semidirect |
| 12. 3−1+2×#4294 | C3 | semidirect |
| 13. #17987402 | C3 | semidirect |
| 14. C3×C9×#4294 | C3 | semidirect |
| 69. C3×#4294 | 3−1+2 | semidirect |
| 104. C9×C19 | #737 | semidirect |
| 114. #4294 | #737 | semidirect |
| 183. C19 | #10624879 | semidirect |
| 203. C9 | #13095331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095331 | 3 |
| #17987468 | 3 |
| #17987460 | 3 |
| #17987447 | 3 |
| #17987446 | 3 |
| #17987441 | 3 |
| #17987440 | 3 |
| #17987439 | 3 |
| #17987438 | 3 |
| #17987423 | 3 |
| #17987415 | 3 |
| 3−1+2×#4294 | 3 |
| #17987402 | 3 |
| C3×C9×#4294 | 3 |
| C19×C9⋊H(3,𝔽3) | 3 |
| #10624879 | 19 |