Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 118 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×C32×C5×D4 | C2 | semidirect |
| 2. C2×C3×#1220 | C2 | semidirect |
| 3. C2×C3×D60 | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. #91829 | C3 | direct (N × H) |
| 16. C2×C3×C5×D4 | D3 | semidirect |
| 17. C2×C3×C5×D4 | C2×C3 | semidirect |
| 18. C2×#1220 | C2×C3 | semidirect |
| 19. C2×D60 | C2×C3 | semidirect |
| 22. C4×Dic15 | C2×C3 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 30. C3×Dic15 | D4 | semidirect |
| 32. C2×C32×D4 | D5 | semidirect |
| 59. C2×C5×D4 | C3×D3 | semidirect |
| 84. C3×C4×C5 | #67 | semidirect |
| 85. C3×C4×C5 | C3×D4 | semidirect |
| 86. Dic15 | C3×D4 | semidirect |
| 91. C2×C3×D4 | C3×D5 | semidirect |
| 92. C2×C3×D4 | D15 | semidirect |
| 97. C32×C5 | #127 | semidirect |
| 110. C32×C4 | C22⋊D5 | semidirect |
| 146. C4×C5 | C3×#67 | semidirect |
| 154. C2×D4 | C3×D15 | semidirect |
| 157. C3×C5 | #940 | semidirect |
| 158. C3×C5 | C3×#127 | semidirect |
| 174. C3×C4 | C3×C22⋊D5 | semidirect |
| 175. C3×C4 | #1220 | semidirect |
| 181. C32 | #4086 | semidirect |
| 200. C5 | C3×#940 | semidirect |
| 207. C4 | C3×#1220 | semidirect |
| 209. C3 | C3×#4086 | semidirect |
| 210. C3 | #91829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C3×#1220 | 2 |
| C2×C3×D60 | 2 |
| C3×C4×Dic15 | 2 |
| #91829 | 3 |
| C3×#4086 | 3 |
| C3×#940 | 5 |