Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
957 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 957 conjugacy classes of subgroups — too many to draw. Only its 182 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×#4557 | C2 | semidirect |
| 4. #10589157 | C2 | semidirect |
| 11. C2×#3743 | C4 | semidirect |
| 12. C2×C8×C3⋊D3 | C4 | semidirect |
| 17. C4×#624 | C4 | semidirect |
| 18. #63874 | C4 | semidirect |
| 24. #4557 | D3 | semidirect |
| 39. C2×C32×C8 | C2×C4 | semidirect |
| 41. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 47. C3×C4×Dic3 | C2×C4 | semidirect |
| 132. C2×C3×C8 | C4×D3 | semidirect |
| 141. C4×Dic3 | C4×D3 | semidirect |
| 243. C3⋊D3 | H(3,ℤ/4) | semidirect |
| 262. C2×C8 | #624 | semidirect |
| 303. C32 | C2×H(3,ℤ/4) | semidirect |
| 362. C3 | D3×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C3⋊D3 | 2 |
| #10594969 | 2 |
| C3×#4557 | 2 |
| #10589157 | 2 |
| D3×H(3,ℤ/4) | 3 |