Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#459 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #459 | D47 |
| hypocenter | C47 | #3284 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094043 | C2 | semidirect |
| 2. #15689793 | C2 | semidirect |
| 3. #15689777 | C2 | semidirect |
| 4. #15689495 | C2 | semidirect |
| 5. #15689351 | C2 | semidirect |
| 6. #15689334 | C2 | semidirect |
| 7. #15689286 | C2 | semidirect |
| 8. #15689265 | C2 | semidirect |
| 9. C4×#10625335 | C2 | semidirect |
| 10. #15689188 | C2 | semidirect |
| 11. C47×#459 | C2 | semidirect |
| 68. #10625335 | D4 | semidirect |
| 127. C4×C47 | #135 | semidirect |
| 147. #459 | D47 | semidirect |
| 152. C47 | #3284 | semidirect |
| 272. C4 | #13094043 | semidirect |