Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. C7×Q8×D5 | C2 | semidirect |
| 3. C5×C7×Q16 | C2 | semidirect |
| 4. C7×#689 | C2 | semidirect |
| 5. C7×#688 | C2 | semidirect |
| 6. C7×#677 | C2 | semidirect |
| 7. C7×#676 | C2 | semidirect |
| 20. #4064 | C7 | direct (N × H) |
| 31. C7×Q16 | D5 | semidirect |
| 36. Q8×D5 | C2×C7 | semidirect |
| 37. C5×Q16 | C2×C7 | semidirect |
| 38. #689 | C2×C7 | semidirect |
| 39. #688 | C2×C7 | semidirect |
| 40. #677 | C2×C7 | semidirect |
| 41. #676 | C2×C7 | semidirect |
| 67. C5×C7 | #137 | semidirect |
| 86. Q16 | C7×D5 | semidirect |
| 107. C7 | #4064 | direct (N × H) |
| 108. C5 | C7×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#713 | 2 |
| C7×Q8×D5 | 2 |
| C5×C7×Q16 | 2 |
| C7×#689 | 2 |
| C7×#688 | 2 |
| C7×#677 | 2 |
| C7×#676 | 2 |
| C7×#137 | 5 |
| #4064 | 7 |