Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 1. C7×#713 | C2 | semidirect |
| 2. C7×D4×D5 | C2 | semidirect |
| 3. C5×C7×SD16 | C2 | semidirect |
| 4. C7×#688 | C2 | semidirect |
| 5. C7×#686 | C2 | semidirect |
| 6. C7×D40 | C2 | semidirect |
| 7. C7×#676 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 14. C7×D20 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C7×#168 | C22 | semidirect |
| 20. #4060 | C7 | direct (N × H) |
| 32. C7×SD16 | D5 | semidirect |
| 36. #713 | C2×C7 | semidirect |
| 37. D4×D5 | C2×C7 | semidirect |
| 38. C5×SD16 | C2×C7 | semidirect |
| 39. #688 | C2×C7 | semidirect |
| 40. #686 | C2×C7 | semidirect |
| 41. D40 | C2×C7 | semidirect |
| 42. #676 | C2×C7 | semidirect |
| 49. C7×Q8 | C2×D5 | semidirect |
| 58. C7×C8 | C2×D5 | semidirect |
| 60. C5×Q8 | C22×C7 | semidirect |
| 65. D20 | C22×C7 | semidirect |
| 68. C5×C8 | C22×C7 | semidirect |
| 69. #168 | C22×C7 | semidirect |
| 70. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 91. SD16 | C7×D5 | semidirect |
| 106. Q8 | C2×C7×D5 | semidirect |
| 115. C8 | C2×C7×D5 | semidirect |
| 116. C7 | #4060 | direct (N × H) |
| 117. C5 | C7×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#713 | 2 |
| C7×D4×D5 | 2 |
| C5×C7×SD16 | 2 |
| C7×#688 | 2 |
| C7×#686 | 2 |
| C7×D40 | 2 |
| C7×#676 | 2 |
| C7×AGL(1,ℤ/8) | 5 |
| #4060 | 7 |