Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. #10587906 | C2 | semidirect |
| 4. #10587905 | C2 | semidirect |
| 5. #10587898 | C2 | semidirect |
| 23. C2×C7×Q8 | D5 | semidirect |
| 28. C2×C5×Q8 | D7 | semidirect |
| 54. C5×C7 | #137 | semidirect |
| 69. C2×Q8 | D35 | semidirect |
| 88. C7 | #4088 | semidirect |
| 89. C5 | #6505 | 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 |
| #10587987 | 2 |
| #10587906 | 2 |
| #10587905 | 2 |
| #10587898 | 2 |
| #6505 | 5 |
| #4088 | 7 |