Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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. #10592529 | C2 | semidirect |
| 4. C32×#335 | C2 | semidirect |
| 5. #10589350 | C2 | semidirect |
| 7. #10589321 | C2 | semidirect |
| 27. C3×#335 | D3 | semidirect |
| 47. #3744 | C8 | semidirect |
| 77. #634 | C2×C8 | semidirect |
| 81. C32×C8 | C2×C8 | semidirect |
| 88. #335 | C3⋊D3 | semidirect |
| 153. C3×C8 | D3×C8 | semidirect |
| 191. C32 | SD16⋊C8 | semidirect |
| 211. C8 | C8×C3⋊D3 | semidirect |
| 228. C3 | #68558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592533 | 2 |
| #10592529 | 2 |
| C4×#3744 | 2 |
| C32×#335 | 2 |
| #10589350 | 2 |
| #10589349 | 2 |
| #10589321 | 2 |
| #68558 | 3 |