Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 90 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×#67180 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. #10623805 | C2 | direct (N × H) |
| 11. #67180 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 22. C2×C3⋊#168 | D3 | semidirect |
| 54. C3⋊#168 | C2×D3 | semidirect |
| 58. C2×C32×C5 | SD16 | semidirect |
| 98. C32×C5 | C2×SD16 | semidirect |
| 117. C2×C3×C5 | #204 | semidirect |
| 118. C2×C3×C5 | #214 | semidirect |
| 148. C2×C32 | #687 | semidirect |
| 156. C3×C5 | C2×#204 | semidirect |
| 157. C3×C5 | C2×#214 | semidirect |
| 175. C2×C5 | #3716 | semidirect |
| 177. C32 | C2×#687 | semidirect |
| 189. C2×C3 | #6659 | semidirect |
| 190. C2×C3 | #6716 | semidirect |
| 194. C5 | C2×#3716 | semidirect |
| 202. C3 | C2×#6659 | semidirect |
| 203. C3 | C2×#6716 | semidirect |
| 205. C2 | #10623805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #10623805 | 2 |
| C2×#6716 | 3 |
| C2×#6659 | 3 |
| C2×#3716 | 5 |