Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
577 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 577 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 3. C3×#4455 | C2 | semidirect |
| 4. #10589079 | C2 | semidirect |
| 18. #4455 | D3 | semidirect |
| 27. C8×C3⋊D3 | C8 | semidirect |
| 52. C32×C8 | C2×C8 | semidirect |
| 53. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 109. C3×C8 | D3×C8 | semidirect |
| 115. C3⋊D3 | #322 | semidirect |
| 140. C32 | C2×#322 | semidirect |
| 150. C8 | #3710 | semidirect |
| 165. C3 | D3×#322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C3⋊D3 | 2 |
| C4×#3710 | 2 |
| C3×#4455 | 2 |
| #10589079 | 2 |
| D3×#322 | 3 |