Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×C5×D3×Q8 | C2 | semidirect |
| 3. #10623912 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. #10623809 | C2 | semidirect |
| 6. #10623801 | C2 | semidirect |
| 7. #10623796 | C2 | semidirect |
| 24. C5×D3×Q8 | D3 | semidirect |
| 31. #6717 | D3 | semidirect |
| 45. C3×D3×Q8 | D5 | semidirect |
| 118. D3×Q8 | D15 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #915 | semidirect |
| 203. C3×C5 | #942 | semidirect |
| 224. C32 | #4088 | semidirect |
| 243. C5 | #63946 | semidirect |
| 252. C3 | #91518 | semidirect |
| 253. C3 | #91831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×Q8 | 2 |
| #10624193 | 2 |
| #10623912 | 2 |
| C3×#6717 | 2 |
| #10623809 | 2 |
| #10623801 | 2 |
| #10623796 | 2 |
| #91831 | 3 |
| #91518 | 3 |
| #63946 | 5 |