Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1425 conjugacy classes of subgroups; only the 618 normal subgroups are shown.
This group has 1425 conjugacy classes of subgroups — too many to draw. Only its 618 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. #73311 | C3 | direct (N × H) |
| 23. C32×C42 | Q8 | semidirect |
| 60. C3×C42 | Dic6 | semidirect |
| 63. C3×C42 | C3×Q8 | semidirect |
| 68. C32×C4 | C4⋊Q8 | semidirect |
| 98. C42 | C3×Dic6 | semidirect |
| 109. C3×C4 | #869 | semidirect |
| 112. C3×C4 | C3×C4⋊Q8 | semidirect |
| 114. C32 | #2868 | semidirect |
| 130. C4 | C3×#869 | semidirect |
| 133. C3 | #73311 | direct (N × H) |
| 134. C3 | C3×#2868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#869 | 2 |
| C32×C43 | 2 |
| C3×#4935 | 2 |
| C3×#2868 | 3 |
| #73311 | 3 |