Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D47 |
| commutator | C22×C47 | C25 |
| Frattini | C22 | C24×D47 |
| Fitting | C2×#127×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×#127 | D47 |
| hypocenter | C47 | C2×#560 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689860 | C2 | direct (N × H) |
| 2. C2×#13094018 | C2 | semidirect |
| 3. C2×#13094005 | C2 | semidirect |
| 4. C2×#13093996 | C2 | semidirect |
| 5. C2×#13093992 | C2 | semidirect |
| 6. C2×#127×C47 | C2 | semidirect |
| 9. C23×Dic47 | C22 | semidirect |
| 10. #13094018 | C22 | semidirect |
| 11. #13094005 | C22 | semidirect |
| 12. #13093996 | C22 | semidirect |
| 13. #13093992 | C22 | semidirect |
| 14. C2×Dic47⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic47 | C22 | semidirect |
| 19. C22×D4×C47 | C22 | semidirect |
| 20. #127×C47 | C22 | semidirect |
| 21. C2×C42×C47 | C22 | semidirect |
| 30. C2×D4×C47 | C23 | semidirect |
| 36. C22×Dic47 | C23 | semidirect |
| 37. C42×C47 | C23 | semidirect |
| 39. C22⋊Dic47 | C23 | semidirect |
| 41. Dic47⋊C4 | C23 | semidirect |
| 75. C2×C47 | #560 | semidirect |
| 79. C2×#127 | D47 | semidirect |
| 84. C47 | C2×#560 | semidirect |
| 88. C22×D4 | C2×D47 | semidirect |
| 90. #127 | C2×D47 | semidirect |
| 99. C2×C42 | C2×D47 | semidirect |
| 110. C2×D4 | C22×D47 | semidirect |
| 119. C42 | C22×D47 | semidirect |
| 153. C2 | #15689860 | direct (N × H) |