Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3×Dic30 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. #10623824 | C2 | direct (N × H) |
| 13. C3×Dic30 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 16. C2×Dic30 | D3 | semidirect |
| 21. C2×C3⋊#168 | D3 | semidirect |
| 44. Dic30 | C2×D3 | semidirect |
| 54. C3⋊#168 | C2×D3 | semidirect |
| 58. C2×C32×C5 | SD16 | semidirect |
| 99. C32×C5 | C2×SD16 | semidirect |
| 117. C2×C3×C5 | #204 | semidirect |
| 118. C2×C3×C5 | #215 | semidirect |
| 150. C2×C32 | #687 | semidirect |
| 158. C3×C5 | C2×#204 | semidirect |
| 159. C3×C5 | C2×#215 | semidirect |
| 178. C2×C5 | #3717 | semidirect |
| 180. C32 | C2×#687 | semidirect |
| 191. C2×C3 | #6656 | semidirect |
| 192. C2×C3 | #6659 | semidirect |
| 198. C5 | C2×#3717 | semidirect |
| 206. C3 | C2×#6656 | semidirect |
| 207. C3 | C2×#6659 | semidirect |
| 209. C2 | #10623824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C3×Dic30 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #10623824 | 2 |
| C2×#6659 | 3 |
| C2×#6656 | 3 |
| C2×#3717 | 5 |