Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4×C5×C7 | C2 | semidirect |
| 3. C2×C4×D35 | C2 | semidirect |
| 4. C22⋊Dic35 | C2 | semidirect |
| 5. #10587902 | C2 | semidirect |
| 6. #10587900 | C2 | semidirect |
| 7. C4×Dic35 | C2 | semidirect |
| 13. C22⋊D35 | C4 | direct (N × H) |
| 22. C22×C5×C7 | C2×C4 | semidirect |
| 26. C2×D35 | C2×C4 | semidirect |
| 28. C4×C5×C7 | D4 | semidirect |
| 31. Dic35 | C2×C4 | semidirect |
| 32. C22×C4×C7 | D5 | semidirect |
| 39. C22×C4×C5 | D7 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 75. C22×C7 | C4×D5 | semidirect |
| 81. C4×C7 | C22⋊D5 | semidirect |
| 87. C22×C5 | C4×D7 | semidirect |
| 93. C4×C5 | C22⋊D7 | semidirect |
| 99. C22×C4 | D35 | semidirect |
| 124. C7 | C4×C22⋊D5 | semidirect |
| 125. C5 | C4×C22⋊D7 | semidirect |
| 131. C22 | C4×D35 | semidirect |
| 137. C4 | C22⋊D35 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C7 | 2 |
| C2×C22⋊D35 | 2 |
| C2×C4×D35 | 2 |
| C22⋊Dic35 | 2 |
| #10587902 | 2 |
| #10587900 | 2 |
| C4×Dic35 | 2 |
| C4×C22⋊D7 | 5 |
| C4×C22⋊D5 | 7 |