Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1188 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 265 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×C4×M16 | C2 | semidirect |
| 3. C2×#63650 | C2 | semidirect |
| 4. #10592623 | C2 | semidirect |
| 19. C3×C4×M16 | D3 | semidirect |
| 33. C32×M16 | D4 | semidirect |
| 74. C4×M16 | C3⋊D3 | semidirect |
| 86. C3×M16 | D12 | semidirect |
| 100. C32×C4 | #100 | semidirect |
| 150. M16 | C4⋊(C3⋊D3) | semidirect |
| 163. C3×C4 | #823 | semidirect |
| 167. C32 | #1965 | semidirect |
| 197. C4 | #63650 | semidirect |
| 201. C3 | #69876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64083 | 2 |
| C32×C4×M16 | 2 |
| C2×#63650 | 2 |
| #10592623 | 2 |
| #69876 | 3 |