Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1272 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 297 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×#500 | C2 | semidirect |
| 3. #10592777 | C2 | semidirect |
| 5. #10592573 | C2 | semidirect |
| 7. #10592381 | C2 | semidirect |
| 26. C3×#500 | D3 | semidirect |
| 52. C8×C3⋊D3 | Q8 | semidirect |
| 86. C32×C8 | C2×Q8 | semidirect |
| 87. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 92. #500 | C3⋊D3 | direct (N × H) |
| 160. C3×C8 | D3×Q8 | semidirect |
| 165. C3⋊D3 | #500 | direct (N × H) |
| 199. C32 | C2×#500 | semidirect |
| 217. C8 | Q8×C3⋊D3 | semidirect |
| 234. C3 | D3×#500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×C4⋊Q8 | 2 |
| C32×#500 | 2 |
| #10592777 | 2 |
| C3⋊D3×#107 | 2 |
| #10592573 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #10592381 | 2 |
| D3×#500 | 3 |