Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3213 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 | C2×2−1+4×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C2×2−1+4 | D59 |
| hypocenter | C59 | C22×2−1+4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273775 | C2 | semidirect |
| 2. C2×#14273774 | C2 | semidirect |
| 3. 2−1+4×D59 | C2 | direct (N × H) |
| 4. C2×#41×D59 | C2 | semidirect |
| 5. C22×Q8×D59 | C2 | semidirect |
| 6. C2×2−1+4×C59 | C2 | semidirect |
| 7. #14273775 | C22 | semidirect |
| 8. #14273774 | C22 | semidirect |
| 9. C2×#11745689 | C22 | semidirect |
| 10. C2×#11745685 | C22 | semidirect |
| 11. C2×#11745687 | C22 | semidirect |
| 12. #41×D59 | C22 | semidirect |
| 13. C22×Dic118 | C22 | semidirect |
| 15. C2×Q8×D59 | C22 | semidirect |
| 16. C2×Q8×D59 | C22 | semidirect |
| 19. 2−1+4×C59 | C22 | semidirect |
| 20. C2×#41×C59 | C22 | semidirect |
| 21. C22×Q8×C59 | C22 | semidirect |
| 23. #41×C59 | C23 | semidirect |
| 25. C2×Q8×C59 | C23 | semidirect |
| 30. #11745689 | C23 | semidirect |
| 32. Q8×D59 | C23 | semidirect |
| 33. #11745687 | C23 | semidirect |
| 35. #11745685 | C23 | semidirect |
| 41. C2×Dic118 | C23 | semidirect |
| 63. C2×D59 | 2−1+4 | direct (N × H) |
| 70. C2×C59 | C2×2−1+4 | semidirect |
| 73. D59 | C2×2−1+4 | direct (N × H) |
| 77. C2×2−1+4 | D59 | direct (N × H) |
| 80. C59 | C22×2−1+4 | semidirect |
| 83. 2−1+4 | C2×D59 | direct (N × H) |
| 88. C2×#41 | C2×D59 | semidirect |
| 93. C22×Q8 | C2×D59 | semidirect |
| 100. #41 | C22×D59 | semidirect |
| 106. C2×Q8 | C22×D59 | semidirect |
| 145. C2 | 2−1+4×D59 | direct (N × H) |