Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×Dic35 | C2 | semidirect |
| 3. C2×D7×Dic5 | C2 | semidirect |
| 4. C7×C22⋊Dic5 | C2 | semidirect |
| 5. Dic7⋊Dic5 | C2 | semidirect |
| 6. (C2×D7)⋊Dic5 | C2 | semidirect |
| 7. Dic5×Dic7 | C2 | semidirect |
| 15. C5×C22⋊D7 | C4 | semidirect |
| 22. C22×C5×C7 | C2×C4 | semidirect |
| 26. C2×C5×D7 | C2×C4 | semidirect |
| 28. Dic35 | D4 | semidirect |
| 29. C5×Dic7 | C2×C4 | semidirect |
| 43. C22⋊Dic5 | D7 | semidirect |
| 55. C22⋊D7 | Dic5 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 75. C22×C7 | C2×Dic5 | semidirect |
| 79. C2×D7 | C2×Dic5 | semidirect |
| 84. Dic7 | C2×Dic5 | semidirect |
| 90. C22×C5 | C4×D7 | semidirect |
| 124. C7 | D4×Dic5 | semidirect |
| 125. C5 | (C22⋊D7)⋊C4 | semidirect |
| 131. C22 | D7×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic35 | 2 |
| C2×C5×C22⋊D7 | 2 |
| C2×D7×Dic5 | 2 |
| C7×C22⋊Dic5 | 2 |
| Dic7⋊Dic5 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| Dic5×Dic7 | 2 |
| (C22⋊D7)⋊C4 | 5 |
| D4×Dic5 | 7 |