Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 132 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×#67141 | C2 | semidirect |
| 5. #10623775 | C2 | semidirect |
| 6. #10623774 | C2 | semidirect |
| 7. #10623773 | C2 | semidirect |
| 28. C22×C32×C5 | Q8 | semidirect |
| 76. C22×C3×C5 | Dic6 | semidirect |
| 91. C32×C5 | C22⋊Q8 | semidirect |
| 103. C22×C32 | Dic10 | semidirect |
| 127. C22×C5 | #634 | semidirect |
| 146. C3×C5 | #878 | semidirect |
| 149. C22×C3 | #1204 | semidirect |
| 161. C32 | #4070 | semidirect |
| 175. C5 | #64087 | semidirect |
| 178. C22 | #67141 | semidirect |
| 186. C3 | #91575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×#67141 | 2 |
| #10623913 | 2 |
| C32×C22⋊Dic5 | 2 |
| #10623775 | 2 |
| #10623774 | 2 |
| #10623773 | 2 |
| #91575 | 3 |
| #64087 | 5 |