Finite Group DatabasebetaFinite Group DatabasebetaOrder 5312.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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 | C23×D83 |
| commutator, socle | C22×C83 | C24 |
| Fitting | #124×C83 | C2 |
| hypercenter | #124 | D83 |
| hypocenter | C83 | #538 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14581786 | C2 | semidirect |
| 2. #14581785 | C2 | semidirect |
| 3. #14581781 | C2 | semidirect |
| 4. #14581776 | C2 | semidirect |
| 5. #14581774 | C2 | semidirect |
| 6. #14581768 | C2 | semidirect |
| 7. #14581765 | C2 | semidirect |
| 8. #14581765 | C2 | semidirect |
| 9. #14581764 | C2 | semidirect |
| 10. #14581762 | C2 | semidirect |
| 11. #14581760 | C2 | semidirect |
| 12. C4×D332 | C2 | semidirect |
| 13. (C22⋊D83)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D83 | C2 | semidirect |
| 15. #124×C83 | C2 | semidirect |
| 22. C2×C22⋊D83 | C22 | semidirect |
| 23. C22×Dic83 | C22 | semidirect |
| 26. C2×C4×D83 | C22 | semidirect |
| 27. C4⋊Dic83 | C22 | semidirect |
| 28. C4⋊Dic83 | C22 | semidirect |
| 29. Dic83⋊C4 | C22 | semidirect |
| 30. Dic83⋊C4 | C22 | semidirect |
| 31. Dic83⋊C4 | C22 | semidirect |
| 32. Dic83⋊C4 | C22 | semidirect |
| 41. (C2×D83)⋊C4 | C22 | semidirect |
| 42. (C2×D83)⋊C4 | C22 | semidirect |
| 43. C4×Dic83 | C22 | semidirect |
| 44. C2×Q8×C83 | C22 | semidirect |
| 48. C22⋊C4×C83 | C22 | semidirect |
| 49. C22⋊C4×C83 | C22 | semidirect |
| 50. C42×C83 | C22 | semidirect |
| 116. C83 | #538 | semidirect |
| 121. #124 | D83 | semidirect |
| 134. C2×Q8 | C2×D83 | semidirect |
| 164. C22⋊C4 | C2×D83 | semidirect |
| 165. C22⋊C4 | C2×D83 | semidirect |
| 167. C42 | C2×D83 | semidirect |