Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #17987549 | C3 | 1 | 3 | yes | maximal, complemented |
| 2 | C19⋊C3×C81 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C27×C19⋊C3 | C9 | 1 | 1 | yes | characteristic |
| 4 | #13095301 | C9 | 1 | 1 | yes | characteristic |
| 5 | #13095301 | C32 | 1 | 1 | yes | characteristic |
| 6 | C19×C81 | C9 | 1 | 1 | yes | characteristic |
| 7 | C243⋊C3 | — | 19 | 1 | no | maximal, Sylow |
| 8 | C9×C19⋊C3 | C27 | 1 | 1 | yes | characteristic |
| 9 | C19×C27 | C3×C9 | 1 | 1 | yes | characteristic |
| 10 | #10587018 | C27 | 1 | 2 | yes | — |
| 11 | C3×C81 | — | 19 | 1 | no | — |
| 12 | C243 | — | 19 | 3 | no | — |
| 13 | C3×C19⋊C3 | C81 | 1 | 1 | yes | characteristic |
| 14 | C9×C19 | C3×C27 | 1 | 1 | yes | characteristic |
| 15 | #4294 | C81 | 1 | 2 | yes | — |
| 16 | C3×C27 | — | 19 | 1 | no | — |
| 17 | C81 | — | 19 | 1 | no | — |
| 18 | C81 | — | 19 | 1 | no | — |
| 19 | C81 | #4296 | 1 | 1 | yes | characteristic |
| 20 | C3×C19 | C3×C81 | 1 | 1 | yes | characteristic |
| 21 | C19⋊C3 | — | 3 | 1 | no | — |
| 22 | C3×C9 | — | 19 | 1 | no | — |
| 23 | C27 | — | 19 | 2 | no | — |
| 24 | C27 | C3×#4296 | 1 | 1 | yes | characteristic |
| 25 | C19 | C243⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 26 | C32 | — | 19 | 1 | no | — |
| 27 | C9 | — | 19 | 2 | no | — |
| 28 | C9 | (C19⋊C3)⋊C27 | 1 | 1 | yes | characteristic |
| 29 | C3 | — | 57 | 1 | no | — |
| 30 | C3 | (C19⋊C3)⋊C81 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17987549 | C3 | semidirect |
| 25. C19 | C243⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987549 | 3 |
| C19⋊C3×C81 | 3 |
| C243⋊C3 | 19 |