Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. #10623912 | C2 | semidirect |
| 4. C3×#6718 | C2 | semidirect |
| 5. #10623809 | C2 | semidirect |
| 6. #10623807 | C2 | semidirect |
| 31. #6718 | D3 | direct (N × H) |
| 80. C3×C5×D3 | Q16 | semidirect |
| 131. C32×C5 | C2×Q16 | semidirect |
| 155. C5×D3 | #216 | semidirect |
| 189. C3×D3 | #689 | semidirect |
| 198. C3×C5 | D3×Q16 | semidirect |
| 199. C3×C5 | C2×#216 | semidirect |
| 219. C32 | C2×#689 | semidirect |
| 235. D3 | #6718 | direct (N × H) |
| 236. C5 | D3×#216 | semidirect |
| 245. C3 | D3×#689 | semidirect |
| 246. C3 | C2×#6718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×Q8 | 2 |
| D3×Dic30 | 2 |
| #10623912 | 2 |
| C3×#6718 | 2 |
| #10623809 | 2 |
| #10623807 | 2 |
| D3×C3⋊#168 | 2 |
| C2×#6718 | 3 |
| D3×#689 | 3 |
| D3×#216 | 5 |