Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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×#441 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #441 | D47 |
| hypocenter | C47 | #2943 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#10625354 | C2 | semidirect |
| 3. #15689236 | C2 | semidirect |
| 4. #15689234 | C2 | semidirect |
| 5. #15689230 | C2 | semidirect |
| 6. #15689226 | C2 | semidirect |
| 7. #15689221 | C2 | semidirect |
| 8. #15689158 | C2 | semidirect |
| 9. #15689118 | C2 | semidirect |
| 10. #97×D47 | C2 | semidirect |
| 11. C47×#441 | C2 | semidirect |
| 13. #13094047 | C4 | semidirect |
| 42. #10625354 | C2×C4 | semidirect |
| 50. Q16×C47 | C2×C4 | semidirect |
| 57. #10625336 | C2×C4 | semidirect |
| 69. D376 | C2×C4 | semidirect |
| 71. C8×D47 | C2×C4 | semidirect |
| 120. #441 | D47 | semidirect |
| 126. C47 | #2943 | semidirect |
| 165. Q16 | C4×D47 | semidirect |