Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1296 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 517 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | C47×#543 | C2 |
| hypercenter | #543 | D47 |
| hypocenter | C47 | C2×#543 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689749 | C2 | semidirect |
| 2. #15689748 | C2 | semidirect |
| 3. C22⋊Q8×D47 | C2 | semidirect |
| 5. C47×#543 | C2 | semidirect |
| 7. C2×Q8×D47 | C22 | semidirect |
| 9. #13094004 | C22 | semidirect |
| 10. #13094003 | C22 | semidirect |
| 11. #13094002 | C22 | semidirect |
| 12. #13094001 | C22 | semidirect |
| 13. #13094000 | C22 | semidirect |
| 14. C4⋊C4×D47 | C22 | semidirect |
| 19. C22⋊Q8×C47 | C22 | semidirect |
| 23. C23×D47 | Q8 | semidirect |
| 26. C2×Q8×C47 | C23 | semidirect |
| 33. C2×Dic94 | C23 | semidirect |
| 34. C4⋊C4×C47 | C23 | semidirect |
| 38. C4⋊Dic47 | C23 | semidirect |
| 39. Dic47⋊C4 | C23 | semidirect |
| 41. C23×C47 | C2×Q8 | semidirect |
| 47. C22×D47 | C2×Q8 | semidirect |
| 75. D47 | #543 | direct (N × H) |
| 78. #543 | D47 | direct (N × H) |
| 81. C47 | C2×#543 | semidirect |
| 90. C22⋊Q8 | C2×D47 | semidirect |
| 104. C2×Q8 | C22×D47 | semidirect |
| 112. C4⋊C4 | C22×D47 | semidirect |
| 124. C23 | Q8×D47 | semidirect |