Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 198 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. C2×C32×Dic10 | C2 | semidirect |
| 3. C32×C42×C5 | C2 | semidirect |
| 4. C32×#685 | C2 | semidirect |
| 5. C3×#4021 | C3 | direct (N × H) |
| 14. C2×C3×Dic10 | C2×C3 | semidirect |
| 15. C3×C42×C5 | C2×C3 | semidirect |
| 16. C3×#685 | C2×C3 | semidirect |
| 23. #4021 | C32 | direct (N × H) |
| 27. C32×C42 | D5 | semidirect |
| 39. C2×Dic10 | C2×C32 | semidirect |
| 40. C42×C5 | C2×C32 | semidirect |
| 41. #685 | C2×C32 | semidirect |
| 57. C3×C42 | C3×D5 | semidirect |
| 58. C32×C5 | #124 | semidirect |
| 93. C42 | C32×D5 | semidirect |
| 94. C3×C5 | C3×#124 | semidirect |
| 104. C32 | #4021 | direct (N × H) |
| 114. C5 | C32×#124 | semidirect |
| 121. C3 | C3×#4021 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D20 | 2 |
| C2×C32×Dic10 | 2 |
| C32×C42×C5 | 2 |
| C32×#685 | 2 |
| C3×#4021 | 3 |
| C32×#124 | 5 |