Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 1. C3×#6817 | C2 | semidirect |
| 2. C32×#709 | C2 | semidirect |
| 3. C2×C3×C5×C3⋊C8 | C2 | semidirect |
| 4. C3×#6662 | C2 | semidirect |
| 5. C3×#6658 | C2 | semidirect |
| 6. C3×#6657 | C2 | semidirect |
| 7. C3×#6653 | C2 | semidirect |
| 9. #91311 | C3 | direct (N × H) |
| 22. #6817 | C2×C3 | semidirect |
| 25. C3×#709 | D3 | semidirect |
| 26. C3×#709 | C2×C3 | semidirect |
| 28. C2×C5×C3⋊C8 | C2×C3 | semidirect |
| 33. #6662 | C2×C3 | semidirect |
| 34. #6658 | C2×C3 | semidirect |
| 35. #6657 | C2×C3 | semidirect |
| 36. #6653 | C2×C3 | semidirect |
| 51. C2×C3×C3⋊C8 | D5 | semidirect |
| 86. #709 | C3×D3 | semidirect |
| 136. C2×C3⋊C8 | C3×D5 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #950 | semidirect |
| 215. C3×C5 | C3×#135 | semidirect |
| 239. C32 | #4050 | semidirect |
| 262. C5 | C3×#950 | semidirect |
| 271. C3 | #91311 | direct (N × H) |
| 272. C3 | C3×#4050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C32×#709 | 2 |
| C2×C3×C5×C3⋊C8 | 2 |
| C3×#6662 | 2 |
| C3×#6658 | 2 |
| C3×#6657 | 2 |
| C3×#6653 | 2 |
| C3×#4050 | 3 |
| #91311 | 3 |
| C3×#950 | 5 |