Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
488 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 70 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. #17987515 | C3 | semidirect |
| 2. #17987511 | C3 | semidirect |
| 3. #17987510 | C3 | semidirect |
| 4. #17987506 | C3 | semidirect |
| 5. #17987505 | C3 | semidirect |
| 6. C3×#13095315 | C3 | semidirect |
| 7. #17987418 | C3 | semidirect |
| 8. (C3×C19⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 9. C19×3−1+4 | C3 | semidirect |
| 45. C19×3−1+2 | H(3,𝔽3) | semidirect |
| 50. C3×C9×C19 | H(3,𝔽3) | semidirect |
| 67. 3−1+4 | C19⋊C3 | semidirect |
| 147. 3−1+2 | C32⋊(C19⋊C3) | semidirect |
| 162. C3×C9 | C32⋊(C19⋊C3) | semidirect |
| 163. C19 | #10624749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987515 | 3 |
| #17987511 | 3 |
| #17987510 | 3 |
| #17987506 | 3 |
| #17987505 | 3 |
| C3×#13095315 | 3 |
| #17987418 | 3 |
| (C3×C19⋊C3)⋊H(3,𝔽3) | 3 |
| C19×3−1+4 | 3 |
| #10624749 | 19 |