Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
140 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 15. #63308 | C4 | semidirect |
| 25. C7×Dic5 | Q8 | semidirect |
| 59. C5×C7 | C4×Q8 | semidirect |
| 75. Dic5 | Dic14 | semidirect |
| 98. C7 | #4033 | semidirect |
| 99. C5 | C4×Dic14 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63308 | 2 |
| #10587900 | 2 |
| C4×C7×Dic5 | 2 |
| C5×Dic7⋊C4 | 2 |
| #10587859 | 2 |
| Dic5×Dic7 | 2 |
| C4×Dic14 | 5 |
| #4033 | 7 |