Finite Group DatabasebetaFinite Group DatabasebetaOrder 4200.
152 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #10597182 |
| commutator, hypocenter | C3×C52 | C2×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C2×C4 |
| prime radical | C7×D15⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C22×C7 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C3⋊#1044 | C2 | semidirect |
| 3. C3×C7×#1043 | C2 | semidirect |
| 5. C5×C7×D15 | C4 | semidirect |
| 10. C7×#1043 | D3 | semidirect |
| 11. #10597182 | C7 | direct (N × H) |
| 12. C3×C52×C7 | C2×C4 | semidirect |
| 20. C3⋊#1044 | C2×C7 | semidirect |
| 21. C3×#1043 | C2×C7 | semidirect |
| 23. C7×D15 | AGL(1,𝔽5) | semidirect |
| 28. C52×C7 | C4×D3 | semidirect |
| 30. C5×D15 | C4×C7 | semidirect |
| 38. C3×C5×C7 | C2×AGL(1,𝔽5) | semidirect |
| 41. #1043 | D3×C7 | semidirect |
| 45. C3×C52 | C2×C4×C7 | semidirect |
| 61. C5×C7 | D3×AGL(1,𝔽5) | semidirect |
| 62. D15 | C7×AGL(1,𝔽5) | semidirect |
| 69. C52 | C4×D3×C7 | semidirect |
| 71. C3×C7 | D5⋊AGL(1,𝔽5) | semidirect |
| 77. C3×C5 | C2×C7×AGL(1,𝔽5) | semidirect |
| 88. C7 | #10597182 | direct (N × H) |
| 92. C5 | D3×C7×AGL(1,𝔽5) | semidirect |
| 96. C3 | C7×D5⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D15⋊D5 | 2 |
| C7×C3⋊#1044 | 2 |
| C3×C7×#1043 | 2 |
| C7×D5⋊AGL(1,𝔽5) | 3 |
| D3×C7×AGL(1,𝔽5) | 5 |
| #10597182 | 7 |