Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
| 2. C2×C7×C22⋊D5 | C2 | semidirect |
| 3. C2×C7×D20 | C2 | semidirect |
| 4. C7×#685 | C2 | semidirect |
| 5. C7×C4⋊Dic5 | C2 | semidirect |
| 15. #4076 | C7 | direct (N × H) |
| 18. C22×C5×C7 | D4 | semidirect |
| 24. C4×C5×C7 | D4 | semidirect |
| 28. C22×C4×C7 | D5 | semidirect |
| 31. C22×C4×C5 | C2×C7 | semidirect |
| 32. C2×C22⋊D5 | C2×C7 | semidirect |
| 33. C2×D20 | C2×C7 | semidirect |
| 34. #685 | C2×C7 | semidirect |
| 35. C4⋊Dic5 | C2×C7 | semidirect |
| 57. C5×C7 | #121 | semidirect |
| 64. C22×C7 | D20 | semidirect |
| 68. C4×C7 | C22⋊D5 | semidirect |
| 71. C22×C5 | C7×D4 | semidirect |
| 77. C4×C5 | C7×D4 | semidirect |
| 81. C22×C4 | C7×D5 | semidirect |
| 102. C7 | #4076 | direct (N × H) |
| 103. C5 | C7×#121 | semidirect |
| 109. C22 | C7×D20 | semidirect |
| 113. C4 | C7×C22⋊D5 | semidirect |
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×C7×C22⋊D5 | 2 |
| C2×C7×D20 | 2 |
| C7×#685 | 2 |
| C7×C4⋊Dic5 | 2 |
| C7×#121 | 5 |
| #4076 | 7 |