Finite Group DatabasebetaFinite Group DatabasebetaOrder 5040.
108 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C7 | C2×C8 |
| prime radical | C3⋊D3×D35 | C4 |
| cosocle | C7×#4379 | C22 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72217160 | C2 | semidirect |
| 2. C7×#67195 | C2 | semidirect |
| 9. C3⋊D105 | C8 | semidirect |
| 11. C32×D35 | C8 | semidirect |
| 19. #67195 | D7 | semidirect |
| 20. C32×C5×C7 | C2×C8 | semidirect |
| 52. D35 | AGL(1,𝔽9) | semidirect |
| 53. C32×C7 | D5⋊C8 | semidirect |
| 58. C32×C5 | C8×D7 | semidirect |
| 68. C5×C7 | C2×AGL(1,𝔽9) | semidirect |
| 91. C32 | #10587920 | semidirect |
| 95. C7 | D5⋊AGL(1,𝔽9) | semidirect |
| 99. C5 | D7×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72217160 | 2 |
| C7×#67195 | 2 |
| #72217077 | 2 |
| D7×AGL(1,𝔽9) | 5 |
| D5⋊AGL(1,𝔽9) | 7 |
| #10587920 | 9 |