Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
153 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 5. #67589 | C3 | direct (N × H) |
| 9. C32×C32 | C4 | semidirect |
| 10. C3×C3⋊C32 | C4 | semidirect |
| 34. C3×C32 | Dic3 | semidirect |
| 35. C3×C32 | C3×C4 | semidirect |
| 36. C3⋊C32 | C3×C4 | semidirect |
| 68. C32 | C3×Dic3 | semidirect |
| 101. C32 | #1397 | semidirect |
| 118. C3 | #67589 | direct (N × H) |
| 119. C3 | C3×#1397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C32 | 2 |
| C3×Dic3×C16 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C3×#1397 | 3 |
| #67589 | 3 |