Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
678 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 172 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×#67153 | C2 | semidirect |
| 5. C2×C3×#1204 | C2 | semidirect |
| 6. #10624039 | C2 | direct (N × H) |
| 14. #67153 | C22 | semidirect |
| 17. C3×#1204 | C22 | semidirect |
| 23. C2×#1204 | D3 | semidirect |
| 29. C2×C5×C3⋊D3 | Q8 | semidirect |
| 56. #1204 | C2×D3 | semidirect |
| 61. C2×C32×C5 | C2×Q8 | semidirect |
| 63. C5×C3⋊D3 | C2×Q8 | semidirect |
| 103. C32×C5 | C22×Q8 | semidirect |
| 115. C2×C3⋊D3 | Dic10 | semidirect |
| 124. C2×C3×C5 | D3×Q8 | semidirect |
| 153. C2×C32 | C2×Dic10 | semidirect |
| 155. C3⋊D3 | C2×Dic10 | semidirect |
| 163. C3×C5 | C2×D3×Q8 | semidirect |
| 179. C2×C5 | #3797 | semidirect |
| 181. C32 | C22×Dic10 | semidirect |
| 194. C2×C3 | D3×Dic10 | semidirect |
| 198. C5 | C2×#3797 | semidirect |
| 207. C3 | C2×D3×Dic10 | semidirect |
| 209. C2 | #10624039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67155 | 2 |
| C2×#67153 | 2 |
| C2×C5×#624 | 2 |
| C2×C3⋊D3×Dic5 | 2 |
| C2×C3×#1204 | 2 |
| #10624039 | 2 |
| C2×D3×Dic10 | 3 |
| C2×#3797 | 5 |