Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15689002 |
| commutator | C2×C4×C47 | C22×C4 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#568 | C2 |
| socle | C2×C47 | #386 |
| hypercenter | #568 | D47 |
| hypocenter | C47 | #1902 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #15689133 | C2 | semidirect |
| 4. C2×#13093942 | C2 | semidirect |
| 5. #15688895 | C2 | semidirect |
| 6. C47⋊#338 | C2 | semidirect |
| 11. C2×#10625337 | C4 | semidirect |
| 12. C2×#10625335 | C4 | semidirect |
| 115. C47 | #1902 | semidirect |