Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#474 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #474 | D47 |
| hypocenter | C47 | #3330 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #474 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689777 | C2 | semidirect |
| 2. #15689776 | C2 | semidirect |
| 3. #15689475 | C2 | semidirect |
| 4. #15689460 | C2 | semidirect |
| 5. #15689370 | C2 | semidirect |
| 6. #15689329 | C2 | semidirect |
| 7. #15689269 | C2 | semidirect |
| 8. C4×#10625334 | C2 | semidirect |
| 9. #15689200 | C2 | semidirect |
| 10. #15689121 | C2 | semidirect |
| 11. C47×#474 | C2 | semidirect |
| 82. D4×C47 | #41 | semidirect |
| 137. #474 | D47 | semidirect |
| 144. C47 | #3330 | semidirect |
| 222. D4 | #10625354 | semidirect |