Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C3×D60 | C2 | semidirect |
| 3. C5×#3748 | C2 | semidirect |
| 4. #10623825 | C2 | semidirect |
| 5. #10623822 | C2 | semidirect |
| 13. C3×D60 | C22 | semidirect |
| 15. C3×Dic30 | C22 | semidirect |
| 16. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 18. #6817 | D3 | semidirect |
| 19. C2×D60 | D3 | semidirect |
| 39. #3748 | D5 | semidirect |
| 50. D60 | C2×D3 | semidirect |
| 52. Dic30 | C2×D3 | semidirect |
| 81. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 110. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 175. C3×C5 | #932 | semidirect |
| 176. C3×C5 | #949 | semidirect |
| 198. C32 | #4054 | semidirect |
| 218. C5 | #63823 | semidirect |
| 227. C3 | #91301 | semidirect |
| 228. C3 | #91312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C2×C3×D60 | 2 |
| C5×#3748 | 2 |
| #10623825 | 2 |
| #10623822 | 2 |
| #91312 | 3 |
| #91301 | 3 |
| #63823 | 5 |