Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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. C2×#63308 | C2 | semidirect |
| 3. C22⋊Dic35 | C2 | semidirect |
| 4. C7×C22⋊Dic5 | C2 | semidirect |
| 5. (C2×D7)⋊Dic5 | C2 | semidirect |
| 6. (C2×D7)⋊Dic5 | C2 | semidirect |
| 7. Dic5×Dic7 | C2 | semidirect |
| 43. C22⋊Dic5 | D7 | semidirect |
| 68. C5×C7 | #124 | semidirect |
| 120. C7 | #4082 | semidirect |
| 121. C5 | #6448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊D7 | 2 |
| C2×#63308 | 2 |
| C22⋊Dic35 | 2 |
| C7×C22⋊Dic5 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| Dic5×Dic7 | 2 |
| #6448 | 5 |
| #4082 | 7 |