Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 4. #67818 | C3 | direct (N × H) |
| 8. C2×C32×C16 | C4 | semidirect |
| 10. C3×#817 | C4 | semidirect |
| 35. C2×C3×C16 | Dic3 | semidirect |
| 36. C2×C3×C16 | C3×C4 | semidirect |
| 40. #817 | C3×C4 | semidirect |
| 86. C2×C16 | C3×Dic3 | semidirect |
| 147. C32 | #1384 | semidirect |
| 174. C3 | #67818 | direct (N × H) |
| 175. C3 | C3×#1384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M32 | 2 |
| C3×#5106 | 2 |
| C3×#1384 | 3 |
| #67818 | 3 |