Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 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. C32×#689 | C2 | direct (N × H) |
| 5. C2×C3×#689 | C3 | direct (N × H) |
| 17. C3×#689 | C2×C3 | direct (N × H) |
| 24. C2×#689 | C32 | direct (N × H) |
| 38. C2×C32×C5 | Q16 | semidirect |
| 42. #689 | C2×C32 | direct (N × H) |
| 61. C32×C5 | C2×Q16 | semidirect |
| 76. C2×C3×C5 | C3×Q16 | semidirect |
| 91. C2×C32 | #689 | direct (N × H) |
| 97. C3×C5 | C2×C3×Q16 | semidirect |
| 103. C2×C5 | C32×Q16 | semidirect |
| 105. C32 | C2×#689 | direct (N × H) |
| 114. C2×C3 | C3×#689 | direct (N × H) |
| 116. C5 | C2×C32×Q16 | semidirect |
| 122. C3 | C2×C3×#689 | direct (N × H) |
| 123. C2 | C32×#689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C32×Dic10 | 2 |
| C32×#689 | 2 |
| C2×C32×#168 | 2 |
| C2×C3×#689 | 3 |
| C2×C32×Q16 | 5 |