Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
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×D4×C11 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C2×C11×C22⋊D5 | C2 | semidirect |
| 4. C22×C11×Dic5 | C2 | semidirect |
| 5. C11×C22⋊Dic5 | C2 | semidirect |
| 6. C11×#685 | C2 | semidirect |
| 7. C11×#683 | C2 | semidirect |
| 25. C22×C5×C11 | D4 | semidirect |
| 33. C11×Dic5 | D4 | semidirect |
| 36. C2×D4×C11 | D5 | semidirect |
| 41. #4085 | C11 | direct (N × H) |
| 59. C2×C5×D4 | C2×C11 | semidirect |
| 60. C2×C22⋊D5 | C2×C11 | semidirect |
| 61. C2×C22⋊D5 | C2×C11 | semidirect |
| 62. C22×Dic5 | C2×C11 | semidirect |
| 63. C22⋊Dic5 | C2×C11 | semidirect |
| 64. #685 | C2×C11 | semidirect |
| 65. #683 | C2×C11 | semidirect |
| 66. C5×C11 | #121 | semidirect |
| 75. C22×C11 | C22⋊D5 | semidirect |
| 104. C22×C5 | D4×C11 | semidirect |
| 112. Dic5 | D4×C11 | semidirect |
| 115. C2×D4 | D5×C11 | semidirect |
| 120. C11 | #4085 | direct (N × H) |
| 138. C5 | C11×#121 | semidirect |
| 147. C22 | C11×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C22×C11×Dic5 | 2 |
| C11×C22⋊Dic5 | 2 |
| C11×#685 | 2 |
| C11×#683 | 2 |
| C11×#121 | 5 |
| #4085 | 11 |