Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C22×C4⋊C4×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C22×C4⋊C4 | D59 |
| hypocenter | C59 | C22×#117 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273685 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic59 | C2 | semidirect |
| 5. C22×C4×Dic59 | C2 | semidirect |
| 6. C22×C4⋊C4×C59 | C2 | semidirect |
| 10. C22×C4×D59 | C4 | semidirect |
| 12. #14273685 | C22 | direct (N × H) |
| 13. C2×C4⋊Dic59 | C22 | semidirect |
| 15. C2×C4×Dic59 | C22 | semidirect |
| 18. C2×C4⋊C4×C59 | C22 | semidirect |
| 32. C2×C4×D59 | C2×C4 | semidirect |
| 34. C4⋊C4×C59 | C23 | semidirect |
| 36. C4⋊Dic59 | C23 | semidirect |
| 37. C4×Dic59 | C23 | semidirect |
| 55. C4×D59 | C22×C4 | semidirect |
| 56. C22×C59 | #117 | semidirect |
| 70. C2×C59 | C2×#117 | semidirect |
| 78. C22×C4⋊C4 | D59 | semidirect |
| 81. C59 | C22×#117 | semidirect |
| 91. C2×C4⋊C4 | C2×D59 | semidirect |
| 110. C4⋊C4 | C22×D59 | semidirect |
| 135. C22 | #14273685 | direct (N × H) |
| 145. C2 | C2×#14273685 | direct (N × H) |