Finite Group DatabasebetaFinite Group DatabasebetaOrder 6859.
42 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C192 | C19 | 1 | 1 | yes | maximal, characteristic |
| 2 | C361 | C19 | 1 | 19 | yes | maximal, direct product factor |
| 3 | C19 | C361 | 1 | 19 | yes | direct product factor |
| 4 | C19 | C192 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C19 | C192 |
| socle | C192 | C19 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C19 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C361 | C19 | direct (N × H) |
| 3. C19 | C361 | direct (N × H) |