Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C4×Dic35 | C2 | semidirect |
| 4. C5×Dic7⋊C4 | C2 | semidirect |
| 5. Dic7⋊Dic5 | C2 | semidirect |
| 7. Dic5×Dic7 | C2 | semidirect |
| 15. D5×Dic7 | C4 | semidirect |
| 32. Dic7⋊C4 | D5 | semidirect |
| 62. C5×C7 | #117 | semidirect |
| 107. C7 | #4038 | semidirect |
| 108. C5 | #6440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic7 | 2 |
| C4×Dic35 | 2 |
| C7×#685 | 2 |
| C5×Dic7⋊C4 | 2 |
| Dic7⋊Dic5 | 2 |
| #10587855 | 2 |
| Dic5×Dic7 | 2 |
| #6440 | 5 |
| #4038 | 7 |