Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
190 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×#4505 | C2 | semidirect |
| 3. C3×#4499 | C2 | semidirect |
| 5. #67828 | C3 | direct (N × H) |
| 7. C32×Q32 | C4 | semidirect |
| 9. C32×D16 | C4 | semidirect |
| 18. #4505 | C2×C3 | semidirect |
| 19. #4499 | C2×C3 | semidirect |
| 33. C3×Q32 | Dic3 | semidirect |
| 34. C3×Q32 | C3×C4 | semidirect |
| 39. C3×D16 | Dic3 | semidirect |
| 40. C3×D16 | C3×C4 | semidirect |
| 89. Q32 | C3×Dic3 | semidirect |
| 91. D16 | C3×Dic3 | semidirect |
| 146. C32 | #1418 | semidirect |
| 171. C3 | #67828 | direct (N × H) |
| 172. C3 | C3×#1418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#508 | 2 |
| C3×#4505 | 2 |
| C3×#4499 | 2 |
| C3×#1418 | 3 |
| #67828 | 3 |