Finite Group DatabasebetaFinite Group DatabasebetaOrder 64261.
4 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C359 | C179 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C179 | — | 359 | 1 | no | maximal, Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C359 | C179 |
| LCS | G ▷ C359 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C359 | C179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C359 | 179 |
| C179 | 359 |