Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
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×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D61 |
| hypocenter | C61 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840505 | C2 | semidirect |
| 2. #16840504 | C2 | semidirect |
| 3. #124×D61 | C2 | semidirect |
| 4. #120×D61 | C2 | semidirect |
| 5. C61×H(3,𝔽4) | C2 | semidirect |
| 6. C24×D61 | C22 | semidirect |
| 7. C2×Q8×D61 | C22 | semidirect |
| 9. #14519766 | C22 | semidirect |
| 10. #14519765 | C22 | semidirect |
| 11. #14519764 | C22 | semidirect |
| 12. #14519763 | C22 | semidirect |
| 13. #14519747 | C22 | semidirect |
| 14. #14519746 | C22 | semidirect |
| 15. #14519745 | C22 | semidirect |
| 16. C22⋊C4×D61 | C22 | semidirect |
| 17. C42×D61 | C22 | semidirect |
| 18. #124×C61 | C22 | semidirect |
| 19. #120×C61 | C22 | semidirect |
| 20. C24×C61 | C23 | semidirect |
| 23. C23×D61 | C23 | semidirect |
| 24. C2×Q8×C61 | C23 | semidirect |
| 31. C2×Dic122 | C23 | semidirect |
| 32. C22⋊C4×C61 | C23 | semidirect |
| 33. C42×C61 | C23 | semidirect |
| 34. C22⋊Dic61 | C23 | semidirect |
| 35. #11758198 | C23 | semidirect |
| 36. C4×Dic61 | C23 | semidirect |
| 65. D61 | H(3,𝔽4) | direct (N × H) |
| 68. H(3,𝔽4) | D61 | direct (N × H) |
| 71. C61 | C2×H(3,𝔽4) | semidirect |
| 79. #124 | C2×D61 | semidirect |
| 83. #120 | C2×D61 | semidirect |
| 89. C24 | C22×D61 | semidirect |
| 92. C2×Q8 | C22×D61 | semidirect |
| 100. C22⋊C4 | C22×D61 | semidirect |
| 102. C42 | C22×D61 | semidirect |