Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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. C32×M64 | C2 | semidirect |
| 3. C3×#4506 | C2 | semidirect |
| 5. #67604 | C3 | direct (N × H) |
| 15. C3×M64 | D3 | semidirect |
| 16. C3×M64 | C2×C3 | semidirect |
| 18. #4506 | C2×C3 | semidirect |
| 49. M64 | C3×D3 | semidirect |
| 119. C32 | #1419 | semidirect |
| 141. C3 | #67604 | direct (N × H) |
| 142. C3 | C3×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| C32×M64 | 2 |
| C3×#4506 | 2 |
| C3×#1419 | 3 |
| #67604 | 3 |