Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×Dic60 | C2 | semidirect |
| 3. C3×C5×Dic12 | C2 | semidirect |
| 5. C3×#6663 | C2 | semidirect |
| 7. D5×Dic12 | C3 | direct (N × H) |
| 19. Dic60 | C2×C3 | semidirect |
| 20. C5×Dic12 | C2×C3 | semidirect |
| 26. #6663 | C2×C3 | semidirect |
| 37. C3×Dic12 | D5 | direct (N × H) |
| 58. C32×D5 | Q16 | semidirect |
| 94. Dic12 | C3×D5 | direct (N × H) |
| 95. C32×C5 | C2×Q16 | semidirect |
| 113. C3×D5 | Dic12 | direct (N × H) |
| 114. C3×D5 | C3×Q16 | semidirect |
| 145. C3×C5 | C2×Dic12 | semidirect |
| 146. C3×C5 | C2×C3×Q16 | semidirect |
| 161. D5 | C3×Dic12 | direct (N × H) |
| 162. C32 | D5×Q16 | semidirect |
| 176. C5 | C2×C3×Dic12 | semidirect |
| 183. C3 | D5×Dic12 | direct (N × H) |
| 184. C3 | C3×D5×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×Dic6 | 2 |
| C3×Dic60 | 2 |
| C3×C5×Dic12 | 2 |
| C32×C8×D5 | 2 |
| C3×#6663 | 2 |
| C3×D5×Q16 | 3 |
| D5×Dic12 | 3 |
| C2×C3×Dic12 | 5 |