Finite Group DatabasebetaFinite Group DatabasebetaOrder 1701.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#733 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10588039 | C3 | 1 | 2 | yes | maximal |
| 3 | #10588035 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | #6882 | — | 7 | 1 | no | maximal, Sylow |
| 5 | C7×3−1+2 | — | 3 | 1 | no | — |
| 6 | C3×C7×C9 | C32 | 1 | 1 | yes | characteristic |
| 7 | #4430 | — | 3 | 2 | no | — |
| 8 | C3×C7⋊C9 | — | 3 | 1 | no | — |
| 9 | #733 | — | 7 | 2 | no | — |
| 10 | #733 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 11 | C9⋊C9 | — | 7 | 1 | no | — |
| 12 | C32×C7 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 13 | C7×C9 | — | 3 | 1 | no | — |
| 14 | C7×C9 | — | 9 | 1 | no | — |
| 15 | C7⋊C9 | — | 9 | 1 | no | — |
| 16 | C7⋊C9 | — | 9 | 2 | no | — |
| 17 | 3−1+2 | — | 3 | 1 | no | — |
| 18 | 3−1+2 | — | 21 | 2 | no | — |
| 19 | C3×C9 | — | 21 | 1 | no | — |
| 20 | C3×C9 | C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 21 | C3×C7 | — | 3 | 1 | no | — |
| 22 | C3×C7 | #732 | 1 | 1 | yes | characteristic |
| 23 | C32 | C7⋊H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 24 | C9 | — | 3 | 1 | no | — |
| 25 | C9 | — | 9 | 1 | no | — |
| 26 | C9 | — | 63 | 1 | no | — |
| 27 | C9 | — | 63 | 2 | no | — |
| 28 | C7 | #6882 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 29 | C3 | — | 3 | 1 | no | — |
| 30 | C3 | #10588042 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 28. C7 | #6882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#733 | 3 |
| #10588039 | 3 |
| #10588035 | 3 |
| #6882 | 7 |