Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
738 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 185 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. C32×#431 | C2 | semidirect |
| 3. #10592625 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 5. #10589322 | C2 | semidirect |
| 25. C3×#431 | D3 | semidirect |
| 101. #431 | C3⋊D3 | semidirect |
| 239. C32 | #1488 | semidirect |
| 287. C3 | #70763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3828 | 2 |
| C32×#431 | 2 |
| #10592625 | 2 |
| #10589325 | 2 |
| #10589322 | 2 |
| #70763 | 3 |