Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×C5×C7×Q8 | C2 | semidirect |
| 3. C7×#689 | C2 | semidirect |
| 4. C7×#688 | C2 | semidirect |
| 5. C7×#681 | C2 | semidirect |
| 16. #4088 | C7 | direct (N × H) |
| 24. C2×C7×Q8 | D5 | semidirect |
| 28. C2×C5×Q8 | C2×C7 | semidirect |
| 30. #689 | C2×C7 | semidirect |
| 31. #688 | C2×C7 | semidirect |
| 32. #681 | C2×C7 | semidirect |
| 54. C5×C7 | #137 | semidirect |
| 69. C2×Q8 | C7×D5 | semidirect |
| 88. C7 | #4088 | direct (N × H) |
| 89. C5 | C7×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×Q8 | 2 |
| C7×#709 | 2 |
| C7×#689 | 2 |
| C7×#688 | 2 |
| C7×#681 | 2 |
| C7×#137 | 5 |
| #4088 | 7 |