Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
662 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 184 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×C3×C5×Dic3 | C2 | semidirect |
| 3. C5×#3722 | C2 | direct (N × H) |
| 7. C22×C5×C3⋊D3 | C4 | semidirect |
| 10. C2×C3×C5×Dic3 | C22 | semidirect |
| 11. C2×#3722 | C5 | direct (N × H) |
| 15. C22×C5×Dic3 | D3 | semidirect |
| 22. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 26. C22×C3×Dic3 | C2×C5 | semidirect |
| 27. #3722 | C2×C5 | direct (N × H) |
| 40. C2×C5×Dic3 | C2×D3 | semidirect |
| 42. C2×C32×C5 | C22⋊C4 | semidirect |
| 51. C22×C3⋊D3 | C4×C5 | semidirect |
| 54. C2×C3×Dic3 | C22×C5 | semidirect |
| 74. C22×Dic3 | C5×D3 | semidirect |
| 76. C32×C5 | C2×C22⋊C4 | semidirect |
| 88. C2×C3⋊D3 | C2×C4×C5 | semidirect |
| 94. C2×C3×C5 | (C2×D3)⋊C4 | semidirect |
| 112. C2×Dic3 | C2×C5×D3 | semidirect |
| 120. C2×C32 | C5×C22⋊C4 | semidirect |
| 128. C3×C5 | C2×(C2×D3)⋊C4 | semidirect |
| 146. C2×C5 | #3722 | direct (N × H) |
| 149. C32 | C2×C5×C22⋊C4 | semidirect |
| 159. C2×C3 | C5×(C2×D3)⋊C4 | semidirect |
| 165. C5 | C2×#3722 | direct (N × H) |
| 174. C3 | C2×C5×(C2×D3)⋊C4 | semidirect |
| 176. C2 | C5×#3722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C5×#3722 | 2 |
| C2×C5×(C2×D3)⋊C4 | 3 |
| C2×#3722 | 5 |