Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D59 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#430 | C2 |
| socle | C2×C59 | C2×C4×D4 |
| hypercenter | #430 | D59 |
| hypocenter | C59 | #2956 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #430 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16838168 | C2 | semidirect |
| 3. #16837523 | C2 | semidirect |
| 4. #16837518 | C2 | semidirect |
| 5. C2×#14273653 | C2 | semidirect |
| 6. M16×Dic59 | C2 | semidirect |
| 7. C59×#430 | C2 | semidirect |
| 9. #14273760 | C4 | semidirect |
| 10. #14273755 | C4 | semidirect |
| 12. #14273735 | C22 | semidirect |
| 17. #14273653 | C22 | semidirect |
| 18. #14273653 | C22 | semidirect |
| 19. #14273637 | C22 | semidirect |
| 20. C8×Dic59 | C22 | semidirect |
| 23. #108×C59 | C22 | semidirect |
| 44. Dic236 | C2×C4 | semidirect |
| 45. D472 | C2×C4 | semidirect |
| 46. #11745660 | C2×C4 | semidirect |
| 90. #430 | D59 | semidirect |
| 93. C59 | #2956 | semidirect |
| 105. #108 | C2×D59 | semidirect |