Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
394 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 4. #10623906 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. #10623815 | C2 | semidirect |
| 7. #10623814 | C2 | semidirect |
| 19. D3×Dic15 | C4 | semidirect |
| 32. #6712 | D3 | direct (N × H) |
| 42. C3⋊Dic15 | C2×C4 | semidirect |
| 44. C3×Dic15 | C2×C4 | semidirect |
| 82. C3×C5×D3 | C4⋊C4 | semidirect |
| 120. Dic15 | C4×D3 | semidirect |
| 139. C32×C5 | C2×C4⋊C4 | semidirect |
| 171. C5×D3 | Dic3⋊C4 | semidirect |
| 208. C3×D3 | #683 | semidirect |
| 217. C3×C5 | D3×C4⋊C4 | semidirect |
| 218. C3×C5 | C2×Dic3⋊C4 | semidirect |
| 247. C32 | C2×#683 | semidirect |
| 268. D3 | #6712 | direct (N × H) |
| 269. C5 | D3×Dic3⋊C4 | semidirect |
| 281. C3 | D3×#683 | semidirect |
| 282. C3 | C2×#6712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C2×D3×Dic15 | 2 |
| #10623906 | 2 |
| C3×#6712 | 2 |
| #10623815 | 2 |
| #10623814 | 2 |
| C2×#6712 | 3 |
| D3×#683 | 3 |
| D3×Dic3⋊C4 | 5 |