Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
58 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #17987377 | C3 | 1 | 3 | yes | maximal |
| 2 | C9×C19×C27 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13095322 | — | 3 | 3 | no | — |
| 4 | C3×C19×C27 | — | 3 | 1 | no | — |
| 5 | C92×C19 | C32 | 1 | 1 | yes | characteristic |
| 6 | #10624536 | — | 19 | 1 | no | maximal, Sylow |
| 7 | C3×C9×C19 | — | 3 | 1 | no | — |
| 8 | C3×C9×C19 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 9 | #10587025 | — | 9 | 3 | no | — |
| 10 | C19×C27 | — | 3 | 3 | no | — |
| 11 | #6880 | — | 19 | 3 | no | — |
| 12 | C9×C27 | C19⋊C3 | 1 | 1 | yes | characteristic |
| 13 | C32×C19 | #732 | 1 | 1 | yes | characteristic |
| 14 | C9×C19 | — | 3 | 3 | no | — |
| 15 | C9×C19 | — | 3 | 1 | no | — |
| 16 | #4294 | — | 27 | 3 | no | — |
| 17 | #733 | — | 57 | 3 | no | — |
| 18 | C3×C27 | — | 3 | 1 | no | — |
| 19 | C92 | C3×C19⋊C3 | 1 | 1 | yes | characteristic |
| 20 | C3×C19 | — | 3 | 1 | no | — |
| 21 | C3×C19 | #6879 | 1 | 1 | yes | characteristic |
| 22 | 3−1+2 | — | 171 | 3 | no | — |
| 23 | C3×C9 | — | 3 | 1 | no | — |
| 24 | C3×C9 | C32⋊(C19⋊C3) | 1 | 1 | yes | characteristic |
| 25 | C27 | — | 3 | 3 | no | — |
| 26 | C19 | #10624536 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 27 | C32 | #13095320 | 1 | 1 | yes | characteristic |
| 28 | C9 | — | 513 | 3 | no | — |
| 29 | C9 | — | 3 | 3 | no | — |
| 30 | C9 | — | 3 | 1 | no | — |
| 31 | C3 | — | 3 | 1 | no | — |
| 32 | C3 | #17987374 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 26. C19 | #10624536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987377 | 3 |
| C9×C19×C27 | 3 |
| #10624536 | 19 |