Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
732 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. #10595988 | C2 | semidirect |
| 5. C32×H(3,ℤ/4) | C2 | semidirect |
| 6. #10589425 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 28. C3×H(3,ℤ/4) | D3 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | Q8 | semidirect |
| 41. C2×#634 | Q8 | semidirect |
| 111. H(3,ℤ/4) | C3⋊D3 | semidirect |
| 254. C32 | #2031 | semidirect |
| 302. C3 | #68714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595988 | 2 |
| C2×#63652 | 2 |
| #10592705 | 2 |
| #10592704 | 2 |
| C32×H(3,ℤ/4) | 2 |
| #10589425 | 2 |
| #10589398 | 2 |
| #68714 | 3 |