Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 145 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×C32×C5×Q8 | C2 | semidirect |
| 4. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 5. #10623906 | C2 | semidirect |
| 15. C2×C3×C5×Q8 | D3 | semidirect |
| 23. C2×C3⋊D15 | Q8 | semidirect |
| 29. C2×C32×Q8 | D5 | semidirect |
| 46. C2×C5×Q8 | C3⋊D3 | semidirect |
| 66. C2×C3×Q8 | D15 | semidirect |
| 71. C32×C5 | C22⋊Q8 | semidirect |
| 111. C2×Q8 | C3⋊D15 | semidirect |
| 116. C3×C5 | #946 | semidirect |
| 129. C32 | #4092 | semidirect |
| 141. C5 | #64155 | semidirect |
| 150. C3 | #91835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C4×C3⋊D15 | 2 |
| #10623908 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| #10623906 | 2 |
| #91835 | 3 |
| #64155 | 5 |