Finite Group DatabasebetaFinite Group DatabasebetaOrder 7356.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C613⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×C613 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C613⋊C3 | C4 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 4 | C2×C613 | C2×C3 | 1 | 1 | yes | characteristic |
| 5 | C613 | C3×C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C3×C4 | — | 613 | 1 | no | maximal, Hall |
| 7 | C2×C3 | — | 613 | 1 | no | — |
| 8 | C4 | C613⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 9 | C3 | — | 613 | 1 | no | Sylow |
| 10 | C2 | C2×C613⋊C3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C613⋊C3 |
| commutator, hypocenter | C613 | C3×C4 |
| Frattini | C2 | C2×C613⋊C3 |
| Fitting | C4×C613 | C3 |
| socle | C2×C613 | C2×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C613 | C3 | semidirect |
| 3. C613⋊C3 | C4 | direct (N × H) |
| 5. C613 | C3×C4 | semidirect |
| 8. C4 | C613⋊C3 | direct (N × H) |