Finite Group DatabasebetaFinite Group DatabasebetaOrder 34101.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #26015534 | C3 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×C421⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | H(3,𝔽3)×C421 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | C32×C421 | — | 3 | 1 | no | — |
| 5 | C32×C421 | C32 | 1 | 1 | yes | characteristic |
| 6 | C421⋊C9 | — | 3 | 1 | no | — |
| 7 | C421⋊C9 | — | 3 | 2 | no | — |
| 8 | C3×C421 | — | 3 | 1 | no | — |
| 9 | C3×C421 | — | 9 | 1 | no | — |
| 10 | C3×C421 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 11 | C421 | #731 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | #731 | — | 421 | 1 | no | maximal, Sylow |
| 13 | 3−1+2 | — | 421 | 2 | no | — |
| 14 | H(3,𝔽3) | C421⋊C3 | 1 | 1 | yes | characteristic |
| 15 | C3×C9 | — | 421 | 1 | no | — |
| 16 | C32 | — | 3 | 1 | no | — |
| 17 | C32 | C3×C421⋊C3 | 1 | 1 | yes | characteristic |
| 18 | C9 | — | 1263 | 1 | no | — |
| 19 | C9 | — | 1263 | 2 | no | — |
| 20 | C3 | — | 3 | 1 | no | — |
| 21 | C3 | — | 9 | 1 | no | — |
| 22 | C3 | C32⋊(C421⋊C3) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26015534 | C3 | semidirect |
| 2. C3×C421⋊C9 | C3 | semidirect |
| 11. C421 | #731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015534 | 3 |
| C3×C421⋊C9 | 3 |
| H(3,𝔽3)×C421 | 3 |
| #731 | 421 |