Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
506 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 64 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. #17987421 | C3 | semidirect |
| 2. #17987417 | C3 | semidirect |
| 3. C3×C32⋊#4294 | C3 | semidirect |
| 4. #17987309 | C3 | semidirect |
| 5. C32×C19×H(3,𝔽3) | C3 | semidirect |
| 10. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 16. C32⋊#4294 | C32 | semidirect |
| 17. C32⋊#4294 | C32 | semidirect |
| 50. C32×H(3,𝔽3) | C19⋊C3 | semidirect |
| 137. C19 | #10624596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987421 | 3 |
| #17987417 | 3 |
| C3×C32⋊#4294 | 3 |
| #17987309 | 3 |
| C32×C19×H(3,𝔽3) | 3 |
| #10624596 | 19 |