Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 1. C2×C4×C7×D5 | C2 | semidirect |
| 2. C2×C4×C5×D7 | C2 | semidirect |
| 4. C4×Dic35 | C2 | semidirect |
| 5. #10587858 | C2 | semidirect |
| 6. #10587855 | C2 | semidirect |
| 7. (C2×D7)⋊Dic5 | C2 | semidirect |
| 17. #63305 | C4 | direct (N × H) |
| 23. C2×C7×D5 | C2×C4 | semidirect |
| 26. C2×C5×D7 | C2×C4 | semidirect |
| 27. C4×C5×C7 | D4 | semidirect |
| 29. Dic35 | C2×C4 | semidirect |
| 34. C2×C4×D7 | D5 | semidirect |
| 41. C2×C4×D5 | D7 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 79. C2×D7 | C4×D5 | semidirect |
| 81. C4×C7 | C22⋊D5 | semidirect |
| 91. C2×D5 | C4×D7 | semidirect |
| 93. C4×C5 | C22⋊D7 | semidirect |
| 124. C7 | C4×C22⋊D5 | semidirect |
| 125. C5 | C4×C22⋊D7 | semidirect |
| 137. C4 | #63305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D5 | 2 |
| C2×C4×C5×D7 | 2 |
| C2×#63305 | 2 |
| C4×Dic35 | 2 |
| #10587858 | 2 |
| #10587855 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| C4×C22⋊D7 | 5 |
| C4×C22⋊D5 | 7 |