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. C2×C5×C7×D4 | C2 | semidirect |
| 2. C2×C5×C22⋊D7 | C2 | semidirect |
| 3. C2×C5×C22⋊D7 | C2 | semidirect |
| 4. C22×C5×Dic7 | C2 | semidirect |
| 5. C5×C22⋊Dic7 | C2 | semidirect |
| 6. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 7. C5×Dic7⋊C4 | C2 | semidirect |
| 19. #6502 | C5 | direct (N × H) |
| 26. C22×C5×C7 | D4 | semidirect |
| 34. C5×Dic7 | D4 | semidirect |
| 35. C2×C7×D4 | C2×C5 | semidirect |
| 36. C2×C22⋊D7 | C2×C5 | semidirect |
| 37. C2×C22⋊D7 | C2×C5 | semidirect |
| 38. C22×Dic7 | C2×C5 | semidirect |
| 39. C22⋊Dic7 | C2×C5 | semidirect |
| 40. (C2×D7)⋊C4 | C2×C5 | semidirect |
| 41. Dic7⋊C4 | C2×C5 | semidirect |
| 44. C2×C5×D4 | D7 | semidirect |
| 77. C5×C7 | #121 | semidirect |
| 84. C22×C7 | C5×D4 | semidirect |
| 92. Dic7 | C5×D4 | semidirect |
| 101. C22×C5 | C22⋊D7 | semidirect |
| 109. C2×D4 | C5×D7 | semidirect |
| 137. C7 | C5×#121 | semidirect |
| 138. C5 | #6502 | direct (N × H) |
| 147. C22 | C5×C22⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C2×C5×C22⋊D7 | 2 |
| C22×C5×Dic7 | 2 |
| C5×C22⋊Dic7 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| C5×Dic7⋊C4 | 2 |
| #6502 | 5 |
| C5×#121 | 7 |