Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 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×D59 |
| commutator | C2×C59 | C24×C4 |
| Fitting | C2×H(5,𝔽2)×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C2×H(5,𝔽2) | D59 |
| hypocenter | C59 | C4×H(5,𝔽2) |
| 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. #16837885 | C2 | semidirect |
| 2. #16837877 | C2 | semidirect |
| 3. #41×Dic59 | C2 | semidirect |
| 4. C2×D4×Dic59 | C2 | semidirect |
| 6. C23×Dic59 | C22 | semidirect |
| 7. Q8×Dic59 | C22 | semidirect |
| 8. Q8×Dic59 | C22 | semidirect |
| 9. D4×Dic59 | C22 | semidirect |
| 10. D4×Dic59 | C22 | semidirect |
| 11. D4×Dic59 | C22 | semidirect |
| 12. #14273686 | C22 | semidirect |
| 13. C2×C4⋊Dic59 | C22 | semidirect |
| 14. C2×C22⋊Dic59 | C22 | semidirect |
| 15. C2×C4×Dic59 | C22 | semidirect |
| 16. H(5,𝔽2)×C59 | C4 | semidirect |
| 20. #41×C59 | C2×C4 | semidirect |
| 22. C2×D4×C59 | C2×C4 | semidirect |
| 36. C23×C59 | C22×C4 | semidirect |
| 38. Q8×C59 | C22×C4 | semidirect |
| 39. D4×C59 | C22×C4 | semidirect |
| 40. C2×C4×C59 | C22×C4 | semidirect |
| 56. Dic59 | H(5,𝔽2) | direct (N × H) |
| 67. C59 | C4×H(5,𝔽2) | semidirect |
| 68. H(5,𝔽2) | Dic59 | direct (N × H) |
| 82. #41 | C2×Dic59 | semidirect |
| 84. C2×D4 | C2×Dic59 | semidirect |
| 98. C23 | C22×Dic59 | semidirect |
| 100. Q8 | C22×Dic59 | semidirect |
| 101. D4 | C22×Dic59 | semidirect |
| 108. C2×C4 | C22×Dic59 | semidirect |