Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator | C22×C47 | C2×C42 |
| Fitting | C47×#336 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | #336 | D47 |
| hypocenter | C47 | #1729 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #15688878 | C2 | semidirect |
| 5. #15688877 | C2 | semidirect |
| 6. #15688877 | C2 | semidirect |
| 7. C47×#336 | C2 | semidirect |
| 11. C2×#10625324 | C4 | semidirect |
| 16. C2×C8×D47 | C4 | semidirect |
| 115. #336 | D47 | semidirect |
| 116. C47 | #1729 | semidirect |