Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
140 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 66 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 | direct (N × H) |
| 19. C4×C5×C7 | Q8 | semidirect |
| 59. C5×C7 | C4×Q8 | semidirect |
| 64. C4×C7 | Dic10 | semidirect |
| 72. C4×C5 | Dic14 | semidirect |
| 98. C7 | C4×Dic10 | semidirect |
| 99. C5 | C4×Dic14 | semidirect |
| 107. C4 | #63308 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63308 | 2 |
| C4×Dic35 | 2 |
| C4×C7×Dic5 | 2 |
| C4×C5×Dic7 | 2 |
| #10587859 | 2 |
| #10587858 | 2 |
| Dic7⋊Dic5 | 2 |
| C4×Dic14 | 5 |
| C4×Dic10 | 7 |