Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#427 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #427 | D47 |
| hypocenter | C47 | #2912 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #15689166 | C2 | semidirect |
| 4. #15689164 | C2 | semidirect |
| 5. #15689158 | C2 | semidirect |
| 6. C2×#13093956 | C2 | semidirect |
| 7. #106×D47 | C2 | semidirect |
| 8. C47×#427 | C2 | semidirect |
| 10. #13094030 | C4 | semidirect |
| 38. C2×C8×C47 | C2×C4 | semidirect |
| 50. #10625329 | C2×C4 | semidirect |
| 52. #10625324 | C2×C4 | semidirect |
| 53. C8×D47 | C2×C4 | semidirect |
| 96. #427 | D47 | semidirect |
| 99. C47 | #2912 | semidirect |
| 133. C2×C8 | C4×D47 | semidirect |