Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
426 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10592381 | C2 | semidirect |
| 4. #10589355 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 25. C32×D8 | Q8 | semidirect |
| 66. C3×D8 | Dic6 | semidirect |
| 115. D8 | #634 | semidirect |
| 134. C32 | #2224 | semidirect |
| 162. C3 | #70886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| #10592381 | 2 |
| #10589428 | 2 |
| #10589355 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #70886 | 3 |