Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 88 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×C32×Dic10 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. C3×#6661 | C2 | semidirect |
| 5. C3×#6656 | C2 | semidirect |
| 7. #91309 | C3 | direct (N × H) |
| 21. C2×C3×Dic10 | D3 | semidirect |
| 22. C2×C3×Dic10 | C2×C3 | semidirect |
| 23. #6710 | C2×C3 | semidirect |
| 27. #6661 | C2×C3 | semidirect |
| 28. #6656 | C2×C3 | semidirect |
| 69. C2×Dic10 | C3×D3 | semidirect |
| 109. C32×C5 | #137 | semidirect |
| 171. C3×C5 | #942 | semidirect |
| 172. C3×C5 | C3×#137 | semidirect |
| 192. C32 | #4097 | semidirect |
| 210. C5 | C3×#942 | semidirect |
| 218. C3 | #91309 | direct (N × H) |
| 219. C3 | C3×#4097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#235 | 2 |
| C2×C32×Dic10 | 2 |
| C3×#6710 | 2 |
| C3×#6661 | 2 |
| C3×#6656 | 2 |
| C3×#4097 | 3 |
| #91309 | 3 |
| C3×#942 | 5 |