Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 2. C2×C3×Dic30 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×#6716 | C2 | semidirect |
| 5. C3×#6710 | C2 | semidirect |
| 6. #91840 | C3 | direct (N × H) |
| 21. C2×Dic30 | C2×C3 | semidirect |
| 23. #6718 | C2×C3 | semidirect |
| 24. #6716 | C2×C3 | semidirect |
| 25. #6710 | C2×C3 | semidirect |
| 111. C32×C5 | #137 | semidirect |
| 175. C3×C5 | #951 | semidirect |
| 176. C3×C5 | C3×#137 | semidirect |
| 197. C32 | #4097 | semidirect |
| 216. C5 | C3×#951 | semidirect |
| 224. C3 | C3×#4097 | semidirect |
| 225. C3 | #91840 | 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 |
| C2×C3×Dic30 | 2 |
| C3×#6718 | 2 |
| C3×#6716 | 2 |
| C3×#6710 | 2 |
| #91840 | 3 |
| C3×#4097 | 3 |
| C3×#951 | 5 |