Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 113 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×#347 | C2 | semidirect |
| 4. #10589377 | C2 | semidirect |
| 5. #10589332 | C2 | semidirect |
| 17. C3×#347 | D3 | semidirect |
| 60. #347 | C3⋊D3 | semidirect |
| 127. C32 | #2165 | semidirect |
| 151. C3 | #69088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592406 | 2 |
| C32×#347 | 2 |
| #10589380 | 2 |
| #10589377 | 2 |
| #10589332 | 2 |
| #69088 | 3 |