Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#341 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | #341 | D59 |
| hypocenter | C59 | #1764 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #341 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #16837360 | C2 | semidirect |
| 5. C2×C8×Dic59 | C2 | semidirect |
| 6. #16837163 | C2 | semidirect |
| 7. C59×#341 | C2 | semidirect |
| 10. #14273735 | C4 | semidirect |
| 16. #14273653 | C4 | semidirect |
| 17. #14273652 | C4 | semidirect |
| 18. #14273649 | C4 | semidirect |
| 104. #341 | D59 | semidirect |
| 106. C59 | #1764 | semidirect |