Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10707078 | C2 | semidirect |
| 3. #10707073 | C2 | semidirect |
| 4. #10682857 | C2 | semidirect |
| 5. #10682659 | C2 | semidirect |
| 6. #10682656 | C2 | semidirect |
| 7. C3×#7333 | C2 | semidirect |
| 30. #7333 | D3 | semidirect |
| 51. #4449 | C8 | semidirect |
| 52. D96 | C8 | semidirect |
| 85. Dic24 | C2×C8 | semidirect |
| 89. D48 | C2×C8 | semidirect |
| 94. C3×C32 | C2×C8 | semidirect |
| 167. C32 | D3×C8 | semidirect |
| 252. C3 | AGL(1,ℤ/32) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10715814 | 2 |
| #10707078 | 2 |
| #10707073 | 2 |
| #10682857 | 2 |
| #10682659 | 2 |
| #10682656 | 2 |
| C3×#7333 | 2 |
| AGL(1,ℤ/32) | 3 |