Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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. C3×#6718 | C2 | semidirect |
| 4. #10623826 | C2 | semidirect |
| 20. #6718 | D3 | semidirect |
| 55. C5×C3⋊D3 | Q16 | semidirect |
| 90. C32×C5 | C2×Q16 | semidirect |
| 134. C3⋊D3 | #689 | semidirect |
| 141. C3×C5 | D3×Q16 | semidirect |
| 156. C32 | C2×#689 | semidirect |
| 170. C5 | #63944 | semidirect |
| 178. C3 | D3×#689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| #10624222 | 2 |
| C3×#6718 | 2 |
| #10623826 | 2 |
| #10623818 | 2 |
| D3×#689 | 3 |
| #63944 | 5 |