Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 225 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. C2×C32×Q32 | C2 | semidirect |
| 3. C2×#63656 | C2 | semidirect |
| 4. C3⋊D3×Q32 | C2 | direct (N × H) |
| 5. C2×#63628 | C2 | semidirect |
| 15. C32×Q32 | C22 | semidirect |
| 17. #63656 | C22 | semidirect |
| 19. #63628 | C22 | semidirect |
| 22. C2×C3×Q32 | D3 | semidirect |
| 53. C3×Q32 | C2×D3 | semidirect |
| 79. C2×Q32 | C3⋊D3 | direct (N × H) |
| 100. C2×C3⋊D3 | Q32 | direct (N × H) |
| 116. Q32 | C2×C3⋊D3 | direct (N × H) |
| 136. C2×C32 | C2×Q32 | semidirect |
| 138. C3⋊D3 | C2×Q32 | direct (N × H) |
| 165. C32 | C22×Q32 | semidirect |
| 182. C2×C3 | D3×Q32 | semidirect |
| 193. C3 | C2×D3×Q32 | semidirect |
| 195. C2 | C3⋊D3×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| C2×C32×Q32 | 2 |
| C2×#63656 | 2 |
| C3⋊D3×Q32 | 2 |
| C2×#63628 | 2 |
| C2×C16×C3⋊D3 | 2 |
| C2×D3×Q32 | 3 |