Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D59 |
| commutator | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C2×H(5,𝔽2)×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C2×H(5,𝔽2) | D59 |
| hypocenter | C59 | C2×#585 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838237 | C2 | direct (N × H) |
| 2. C2×#14273774 | C2 | semidirect |
| 3. C2×#14273772 | C2 | semidirect |
| 4. C22×#11745687 | C2 | semidirect |
| 5. C2×#41×D59 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C59 | C2 | semidirect |
| 7. #14273774 | C22 | semidirect |
| 8. #14273772 | C22 | semidirect |
| 9. C2×#11745689 | C22 | semidirect |
| 10. C2×#11745685 | C22 | semidirect |
| 11. C2×#11745687 | C22 | semidirect |
| 12. C2×#11745687 | C22 | semidirect |
| 13. C2×#11745687 | C22 | semidirect |
| 14. #41×D59 | C22 | semidirect |
| 15. C22×Dic118 | C22 | semidirect |
| 16. C2×Q8×D59 | C22 | semidirect |
| 17. C22×C22⋊D59 | C22 | semidirect |
| 18. C2×D4×D59 | C22 | semidirect |
| 19. C23×Dic59 | C22 | semidirect |
| 20. C22×C4×D59 | C22 | semidirect |
| 21. H(5,𝔽2)×C59 | C22 | semidirect |
| 22. C2×#41×C59 | C22 | semidirect |
| 23. C22×D4×C59 | C22 | semidirect |
| 26. #41×C59 | C23 | semidirect |
| 29. C2×D4×C59 | C23 | semidirect |
| 32. C2×C22⋊D59 | C23 | semidirect |
| 35. C22×Dic59 | C23 | semidirect |
| 36. #11745689 | C23 | semidirect |
| 37. Q8×D59 | C23 | semidirect |
| 38. #11745687 | C23 | semidirect |
| 39. #11745687 | C23 | semidirect |
| 40. D4×D59 | C23 | semidirect |
| 41. #11745685 | C23 | semidirect |
| 45. C2×C4×D59 | C23 | semidirect |
| 47. C2×Dic118 | C23 | semidirect |
| 79. C2×C59 | #585 | semidirect |
| 85. C2×H(5,𝔽2) | D59 | semidirect |
| 88. C59 | C2×#585 | semidirect |
| 91. H(5,𝔽2) | C2×D59 | semidirect |
| 98. C2×#41 | C2×D59 | semidirect |
| 103. C22×D4 | C2×D59 | semidirect |
| 112. #41 | C22×D59 | semidirect |
| 122. C2×D4 | C22×D59 | semidirect |
| 161. C2 | #16838237 | direct (N × H) |