Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
984 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 224 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×#67180 | C2 | semidirect |
| 2. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 3. C2×C32×D20 | C2 | semidirect |
| 4. C2×#67138 | C2 | semidirect |
| 5. C2×D5×C3⋊Dic3 | C2 | semidirect |
| 6. #10624148 | C2 | direct (N × H) |
| 12. #67180 | C22 | semidirect |
| 14. C4×C5×C3⋊D3 | C22 | semidirect |
| 15. C32×D20 | C22 | semidirect |
| 16. #67138 | C22 | semidirect |
| 17. D5×C3⋊Dic3 | C22 | semidirect |
| 21. C2×C3×D20 | D3 | semidirect |
| 38. C2×C4×C3⋊D3 | D5 | semidirect |
| 47. C3×D20 | C2×D3 | semidirect |
| 51. C2×C32×C5 | #41 | semidirect |
| 58. C2×D20 | C3⋊D3 | semidirect |
| 69. C4×C3⋊D3 | C2×D5 | semidirect |
| 85. C32×C5 | C2×#41 | semidirect |
| 93. D20 | C2×C3⋊D3 | semidirect |
| 105. C2×C3×C5 | #237 | semidirect |
| 128. C2×C32 | #709 | semidirect |
| 137. C3×C5 | C2×#237 | semidirect |
| 147. C2×C5 | #3830 | semidirect |
| 150. C32 | C2×#709 | semidirect |
| 162. C2×C3 | #6765 | semidirect |
| 165. C5 | C2×#3830 | semidirect |
| 174. C3 | C2×#6765 | semidirect |
| 177. C2 | #10624148 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C32×D20 | 2 |
| C2×#67138 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| #10624148 | 2 |
| C2×#6765 | 3 |
| C2×#3830 | 5 |