Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 285 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. C2×#63664 | C2 | semidirect |
| 3. C42×C3⋊Dic3 | C2 | semidirect |
| 4. #10592623 | C2 | semidirect |
| 7. C32×C4⋊Q8 | C4 | semidirect |
| 8. C32×#127 | C4 | semidirect |
| 9. C32×#124 | C4 | semidirect |
| 39. C4×C3⋊Dic3 | D4 | semidirect |
| 44. C3×C4⋊Q8 | Dic3 | semidirect |
| 45. C3×#127 | Dic3 | semidirect |
| 46. C3×#124 | Dic3 | semidirect |
| 105. C32×C4 | #104 | semidirect |
| 112. C4⋊Q8 | C3⋊Dic3 | semidirect |
| 113. #127 | C3⋊Dic3 | semidirect |
| 114. #124 | C3⋊Dic3 | semidirect |
| 172. C3×C4 | #837 | semidirect |
| 177. C32 | #1962 | semidirect |
| 209. C4 | #63664 | semidirect |
| 213. C3 | #71815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#532 | 2 |
| C2×#63664 | 2 |
| C42×C3⋊Dic3 | 2 |
| #10592623 | 2 |
| #71815 | 3 |