Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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, socle | C22×C59 | C25 |
| Fitting | C59×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D59 |
| hypocenter | C59 | #3549 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838144 | C2 | semidirect |
| 2. #16838114 | C2 | semidirect |
| 3. #16838034 | C2 | semidirect |
| 4. #16837970 | C2 | semidirect |
| 5. #16837967 | C2 | semidirect |
| 6. #16837951 | C2 | semidirect |
| 7. C59×H(3,𝔽4) | C2 | semidirect |
| 8. C2×#11745689 | C22 | semidirect |
| 9. C2×#11745687 | C22 | semidirect |
| 10. C22×C22⋊D59 | C22 | semidirect |
| 11. C2×D4×D59 | C22 | semidirect |
| 12. #14273725 | C22 | semidirect |
| 13. #14273724 | C22 | semidirect |
| 15. #14273723 | C22 | semidirect |
| 16. #14273716 | C22 | semidirect |
| 17. #14273715 | C22 | semidirect |
| 18. #14273713 | C22 | semidirect |
| 19. #14273700 | C22 | semidirect |
| 20. #14273700 | C22 | semidirect |
| 21. #14273699 | C22 | semidirect |
| 22. #14273697 | C22 | semidirect |
| 23. #14273697 | C22 | semidirect |
| 24. #14273696 | C22 | semidirect |
| 25. #14273695 | C22 | semidirect |
| 26. (C22⋊D59)⋊C4 | C22 | semidirect |
| 27. #14273684 | C22 | semidirect |
| 28. #14273683 | C22 | semidirect |
| 29. C42×D59 | C22 | semidirect |
| 30. #124×C59 | C22 | semidirect |
| 31. #124×C59 | C22 | semidirect |
| 32. #120×C59 | C22 | semidirect |
| 103. H(3,𝔽4) | D59 | semidirect |
| 109. C59 | #3549 | semidirect |
| 121. #124 | C2×D59 | semidirect |
| 122. #124 | C2×D59 | semidirect |
| 130. #120 | C2×D59 | semidirect |