Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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×#575 | C2 |
| socle | C2×C59 | C2×C4×D4 |
| hypercenter | #575 | D59 |
| hypocenter | C59 | #2956 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838169 | C2 | semidirect |
| 2. #16837524 | C2 | semidirect |
| 3. #16837519 | C2 | semidirect |
| 4. #16837451 | C2 | semidirect |
| 5. C2×#14273654 | C2 | semidirect |
| 6. M16×Dic59 | C2 | semidirect |
| 9. #14273734 | C22 | semidirect |
| 14. #14273663 | C22 | semidirect |
| 15. #14273654 | C22 | semidirect |
| 16. #14273654 | C22 | semidirect |
| 17. #14273637 | C22 | semidirect |
| 18. C8×Dic59 | C22 | semidirect |
| 20. #137×C59 | C4 | semidirect |
| 21. AGL(1,ℤ/8)×C59 | C4 | semidirect |
| 34. Q16×C59 | C2×C4 | semidirect |
| 35. SD16×C59 | C2×C4 | semidirect |
| 36. D8×C59 | C2×C4 | semidirect |
| 93. C59 | #2956 | semidirect |
| 95. #137 | Dic59 | semidirect |
| 96. AGL(1,ℤ/8) | Dic59 | semidirect |
| 120. Q16 | C2×Dic59 | semidirect |
| 121. SD16 | C2×Dic59 | semidirect |
| 122. D8 | C2×Dic59 | semidirect |