Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 3. C3×Dic60 | C2 | semidirect |
| 4. C3×C5×Dic12 | C2 | semidirect |
| 5. #10623807 | C2 | semidirect |
| 20. Dic60 | D3 | semidirect |
| 24. C5×Dic12 | D3 | semidirect |
| 36. C3×Dic12 | D5 | semidirect |
| 58. C3⋊D15 | Q16 | semidirect |
| 91. Dic12 | D15 | semidirect |
| 95. C32×C5 | C2×Q16 | semidirect |
| 145. C3×C5 | D3×Q16 | semidirect |
| 146. C3×C5 | D3×Q16 | semidirect |
| 162. C32 | D5×Q16 | semidirect |
| 176. C5 | #63802 | semidirect |
| 183. C3 | #91264 | semidirect |
| 184. C3 | Q16×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624198 | 2 |
| C8×C3⋊D15 | 2 |
| C3×Dic60 | 2 |
| C3×C5×Dic12 | 2 |
| #10623807 | 2 |
| Q16×D15 | 3 |
| #91264 | 3 |
| #63802 | 5 |