Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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. C22×C7×Dic5 | C2 | semidirect |
| 3. C2×C4×C7×D5 | C2 | semidirect |
| 4. C5×C7×C22⋊C4 | C2 | semidirect |
| 5. C7×#685 | C2 | semidirect |
| 6. C7×#683 | C2 | semidirect |
| 7. C4×C7×Dic5 | C2 | semidirect |
| 12. C7×C22⋊D5 | C4 | semidirect |
| 19. #4027 | C7 | direct (N × H) |
| 22. C22×C5×C7 | C2×C4 | semidirect |
| 26. C2×C7×D5 | C2×C4 | semidirect |
| 30. C7×Dic5 | C2×C4 | semidirect |
| 31. C7×Dic5 | D4 | semidirect |
| 37. C7×C22⋊C4 | D5 | semidirect |
| 40. C22×Dic5 | C2×C7 | semidirect |
| 41. C2×C4×D5 | C2×C7 | semidirect |
| 42. C5×C22⋊C4 | C2×C7 | semidirect |
| 43. #685 | C2×C7 | semidirect |
| 44. #683 | C2×C7 | semidirect |
| 45. C4×Dic5 | C2×C7 | semidirect |
| 65. C22⋊D5 | C4×C7 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 78. C22×C7 | C4×D5 | semidirect |
| 87. C22×C5 | C2×C4×C7 | semidirect |
| 91. C2×D5 | C2×C4×C7 | semidirect |
| 95. Dic5 | C2×C4×C7 | semidirect |
| 96. Dic5 | C7×D4 | semidirect |
| 102. C22⋊C4 | C7×D5 | semidirect |
| 124. C7 | #4027 | direct (N × H) |
| 125. C5 | C4×C7×D4 | semidirect |
| 131. C22 | C4×C7×D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C22⋊D5 | 2 |
| C22×C7×Dic5 | 2 |
| C2×C4×C7×D5 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C7×#685 | 2 |
| C7×#683 | 2 |
| C4×C7×Dic5 | 2 |
| C4×C7×D4 | 5 |
| #4027 | 7 |