Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D59 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#520 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #520 | D59 |
| hypocenter | C59 | #2897 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #520 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273734 | C2 | semidirect |
| 3. #16837406 | C2 | semidirect |
| 4. #16837401 | C2 | semidirect |
| 5. #16837396 | C2 | semidirect |
| 6. C2×#14273647 | C2 | semidirect |
| 7. C59×#520 | C2 | semidirect |
| 9. #14273773 | C4 | semidirect |
| 15. C2×#11745664 | C22 | semidirect |
| 16. C22×C59⋊C8 | C22 | semidirect |
| 17. #14273650 | C22 | semidirect |
| 18. #14273650 | C22 | semidirect |
| 19. #14273647 | C22 | semidirect |
| 20. #14273647 | C22 | semidirect |
| 21. #14273647 | C22 | semidirect |
| 25. #117×C59 | C22 | semidirect |
| 26. C2×C4⋊C4×C59 | C22 | semidirect |
| 38. #11745685 | C2×C4 | semidirect |
| 41. C2×D236 | C2×C4 | semidirect |
| 100. #520 | D59 | semidirect |
| 105. C59 | #2897 | semidirect |
| 118. #117 | C2×D59 | semidirect |
| 119. C2×C4⋊C4 | C2×D59 | semidirect |