Finite Group DatabasebetaFinite Group DatabasebetaOrder 32428.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C67⋊C121 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C67⋊C121 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | C11×Dic67 | C11 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×C11×C67 | C2×C11 | 1 | 1 | yes | characteristic |
| 5 | C11×C67 | C4×C11 | 1 | 1 | yes | characteristic |
| 6 | C4×C121 | — | 67 | 1 | no | maximal, Hall |
| 7 | Dic67 | C121 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | C2×C121 | — | 67 | 1 | no | — |
| 9 | C2×C67 | C2×C121 | 1 | 1 | yes | characteristic |
| 10 | C121 | — | 67 | 1 | no | Sylow |
| 11 | C67 | C4×C121 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C4×C11 | — | 67 | 1 | no | — |
| 13 | C2×C11 | D67⋊C11 | 1 | 1 | yes | characteristic |
| 14 | C11 | Dic67⋊C11 | 1 | 1 | yes | characteristic |
| 15 | C4 | — | 67 | 1 | no | Sylow |
| 16 | C2 | D67⋊C121 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C11 | D67⋊C11 |
| commutator, hypocenter | C67 | C4×C121 |
| Fitting, socle, prime radical, cosocle | C2×C11×C67 | C2×C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C11 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C67⋊C121 | C4 | semidirect |
| 7. Dic67 | C121 | semidirect |
| 11. C67 | C4×C121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C67⋊C121 | 2 |
| C11×Dic67 | 11 |
| C4×C121 | 67 |