Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
302 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 55 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. #17987419 | C3 | semidirect |
| 3. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 4. C19⋊C3×C32⋊C9 | C3 | semidirect |
| 5. #17987320 | C3 | semidirect |
| 6. #17987320 | C3 | semidirect |
| 7. #17987319 | C3 | semidirect |
| 8. #17987318 | C3 | semidirect |
| 9. C19×#6859 | C3 | semidirect |
| 64. #6859 | C19⋊C3 | semidirect |
| 152. C19 | #10624598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987419 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C19⋊C3×C32⋊C9 | 3 |
| #17987320 | 3 |
| #17987319 | 3 |
| #17987318 | 3 |
| C19×#6859 | 3 |
| #10624598 | 19 |