Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C7⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C4×C7×AGL(1,𝔽5) | C2 | semidirect |
| 5. AGL(1,𝔽5)×Dic7 | C2 | semidirect |
| 9. D7×AGL(1,𝔽5) | C4 | direct (N × H) |
| 10. C4×D35 | C4 | semidirect |
| 12. C4×C5×D7 | C4 | semidirect |
| 13. #63304 | C4 | semidirect |
| 15. D7×Dic5 | C4 | semidirect |
| 22. C7⋊AGL(1,𝔽5) | C2×C4 | semidirect |
| 23. C7×AGL(1,𝔽5) | C2×C4 | semidirect |
| 24. C4×C5×C7 | C2×C4 | semidirect |
| 25. Dic35 | C2×C4 | semidirect |
| 26. C5×Dic7 | C2×C4 | semidirect |
| 27. C7×Dic5 | C2×C4 | semidirect |
| 37. C4×AGL(1,𝔽5) | D7 | direct (N × H) |
| 39. D35 | C42 | semidirect |
| 40. C5×D7 | C42 | semidirect |
| 51. C4×D7 | AGL(1,𝔽5) | direct (N × H) |
| 62. C5×C7 | C2×C42 | semidirect |
| 70. C4×C7 | C2×AGL(1,𝔽5) | semidirect |
| 73. Dic7 | C2×AGL(1,𝔽5) | semidirect |
| 79. AGL(1,𝔽5) | C4×D7 | direct (N × H) |
| 81. C4×C5 | C4×D7 | semidirect |
| 83. Dic5 | C4×D7 | semidirect |
| 92. D7 | C4×AGL(1,𝔽5) | direct (N × H) |
| 107. C7 | C2×C4×AGL(1,𝔽5) | semidirect |
| 108. C5 | C42×D7 | semidirect |
| 118. C4 | D7×AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×AGL(1,𝔽5) | 2 |
| C4×D5×D7 | 2 |
| C4×C7⋊AGL(1,𝔽5) | 2 |
| C4×C7×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×Dic7 | 2 |
| C42×D7 | 5 |
| C2×C4×AGL(1,𝔽5) | 7 |