Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
204 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 52 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. C3×#6762 | C2 | semidirect |
| 3. C32×#704 | C2 | semidirect |
| 5. #91174 | C3 | direct (N × H) |
| 16. #6762 | C2×C3 | semidirect |
| 19. C3×#704 | D3 | semidirect |
| 20. C3×#704 | C2×C3 | semidirect |
| 56. #704 | C3×D3 | semidirect |
| 88. C32×C5 | #100 | semidirect |
| 145. C3×C5 | #823 | semidirect |
| 146. C3×C5 | C3×#100 | semidirect |
| 168. C32 | #4013 | semidirect |
| 186. C5 | C3×#823 | semidirect |
| 195. C3 | #91174 | direct (N × H) |
| 196. C3 | C3×#4013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1203 | 2 |
| C3×#6762 | 2 |
| C32×#704 | 2 |
| C3×#4013 | 3 |
| #91174 | 3 |
| C3×#823 | 5 |