Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 76 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×#67153 | C2 | semidirect |
| 3. C4×C3⋊Dic15 | C2 | semidirect |
| 4. C3×#6714 | C2 | semidirect |
| 5. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. (C2×D3)⋊Dic15 | C2 | semidirect |
| 7. #10623811 | C2 | semidirect |
| 27. #6714 | D3 | semidirect |
| 31. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 52. C3×(C2×D3)⋊C4 | D5 | semidirect |
| 138. (C2×D3)⋊C4 | D15 | semidirect |
| 142. C32×C5 | #124 | semidirect |
| 224. C3×C5 | #885 | semidirect |
| 225. C3×C5 | #885 | semidirect |
| 259. C32 | #4031 | semidirect |
| 282. C5 | #63915 | semidirect |
| 296. C3 | #91464 | semidirect |
| 297. C3 | #91774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67153 | 2 |
| C2×#67150 | 2 |
| C4×C3⋊Dic15 | 2 |
| C3×#6714 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #10623811 | 2 |
| #91774 | 3 |
| #91464 | 3 |
| #63915 | 5 |