Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
930 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 179 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. #10595987 | C2 | semidirect |
| 5. #10592703 | C2 | semidirect |
| 6. C32×H(3,ℤ/4) | C2 | semidirect |
| 7. #10589422 | C2 | semidirect |
| 18. C2×#3746 | C4 | semidirect |
| 19. C2×#3744 | C4 | semidirect |
| 31. C3×H(3,ℤ/4) | D3 | semidirect |
| 121. H(3,ℤ/4) | C3⋊D3 | semidirect |
| 273. C32 | #1905 | semidirect |
| 323. C3 | #68707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64118 | 2 |
| #10595987 | 2 |
| #10592705 | 2 |
| #10592704 | 2 |
| #10592703 | 2 |
| C32×H(3,ℤ/4) | 2 |
| #10589422 | 2 |
| #68707 | 3 |