Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1408 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 459 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×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D47 |
| hypocenter | C47 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689866 | C2 | semidirect |
| 2. #15689865 | C2 | semidirect |
| 3. #124×D47 | C2 | semidirect |
| 4. #120×D47 | C2 | semidirect |
| 5. C47×H(3,𝔽4) | C2 | semidirect |
| 6. C24×D47 | C22 | semidirect |
| 7. C2×Q8×D47 | C22 | semidirect |
| 9. #13094013 | C22 | semidirect |
| 10. #13094012 | C22 | semidirect |
| 11. #13094011 | C22 | semidirect |
| 12. #13094010 | C22 | semidirect |
| 13. #13093994 | C22 | semidirect |
| 14. #13093993 | C22 | semidirect |
| 15. #13093992 | C22 | semidirect |
| 16. C22⋊C4×D47 | C22 | semidirect |
| 17. C42×D47 | C22 | semidirect |
| 18. #124×C47 | C22 | semidirect |
| 19. #120×C47 | C22 | semidirect |
| 20. C24×C47 | C23 | semidirect |
| 23. C23×D47 | C23 | semidirect |
| 24. C2×Q8×C47 | C23 | semidirect |
| 31. C2×Dic94 | C23 | semidirect |
| 32. C22⋊C4×C47 | C23 | semidirect |
| 33. C42×C47 | C23 | semidirect |
| 34. C22⋊Dic47 | C23 | semidirect |
| 35. (C2×D47)⋊C4 | C23 | semidirect |
| 36. C4×Dic47 | C23 | semidirect |
| 65. D47 | H(3,𝔽4) | direct (N × H) |
| 68. H(3,𝔽4) | D47 | direct (N × H) |
| 71. C47 | C2×H(3,𝔽4) | semidirect |
| 79. #124 | C2×D47 | semidirect |
| 83. #120 | C2×D47 | semidirect |
| 89. C24 | C22×D47 | semidirect |
| 92. C2×Q8 | C22×D47 | semidirect |
| 100. C22⋊C4 | C22×D47 | semidirect |
| 102. C42 | C22×D47 | semidirect |