Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10681803 | C2 | semidirect |
| 3. C3×#7456 | C2 | semidirect |
| 13. #7456 | D3 | semidirect |
| 46. Dic24 | C16 | semidirect |
| 48. D48 | C16 | semidirect |
| 157. C3 | #93759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10706949 | 2 |
| #10681803 | 2 |
| C3×#7456 | 2 |
| #93759 | 3 |