Finite Group DatabasebetaFinite Group DatabasebetaOrder 6859.
43 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C192 | C19 | 1 | 20 | yes | maximal, complemented |
| 2 | C19 | — | 19 | 20 | no | — |
| 3 | C19 | C192 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle | C19 | C192 |
| LCS | G ▷ C19 ▷ C1 | |
| UCS | C1 ◁ C19 ◁ G | |
| LECS | G ▷ C19 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C192 | C19 | semidirect |