Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #17987589 | C3 | semidirect |
| 2. C3×C9×#4296 | C3 | semidirect |
| 3. 3−1+2⋊#4296 | C3 | semidirect |
| 14. #13095333 | C9 | semidirect |
| 16. #13095332 | C9 | semidirect |
| 17. #13095331 | C9 | semidirect |
| 23. C19×#737 | C9 | semidirect |
| 79. #737 | #4296 | semidirect |
| 127. C19 | #10624697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987589 | 3 |
| C3×C9×#4296 | 3 |
| 3−1+2⋊#4296 | 3 |
| H(3,𝔽3)⋊#4296 | 3 |
| C19⋊C3×#737 | 3 |
| #10624697 | 19 |