Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×C5×#41 | C2 | semidirect |
| 2. C3×#6817 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. C3×#6716 | C2 | semidirect |
| 6. C3×#6715 | C2 | semidirect |
| 7. C2×C3×C3⋊#168 | C2 | semidirect |
| 8. #91839 | C3 | direct (N × H) |
| 23. C3×C5×#41 | D3 | semidirect |
| 24. C3×C5×#41 | C2×C3 | semidirect |
| 25. #6817 | C2×C3 | semidirect |
| 27. #6718 | C2×C3 | semidirect |
| 28. #6717 | C2×C3 | semidirect |
| 29. #6716 | C2×C3 | semidirect |
| 30. #6715 | C2×C3 | semidirect |
| 31. C2×C3⋊#168 | C2×C3 | semidirect |
| 45. C32×#41 | D5 | semidirect |
| 85. C5×#41 | C3×D3 | semidirect |
| 124. C3×#41 | C3×D5 | semidirect |
| 125. C3×#41 | D15 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 207. #41 | C3×D15 | semidirect |
| 214. C3×C5 | #950 | semidirect |
| 215. C3×C5 | C3×#135 | semidirect |
| 239. C32 | #4096 | semidirect |
| 262. C5 | C3×#950 | semidirect |
| 271. C3 | C3×#4096 | semidirect |
| 272. C3 | #91839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C3×#6817 | 2 |
| C3×#6718 | 2 |
| C3×#6717 | 2 |
| C3×#6716 | 2 |
| C3×#6715 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #91839 | 3 |
| C3×#4096 | 3 |
| C3×#950 | 5 |