Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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. #10592823 | C2 | semidirect |
| 5. C32×H(3,ℤ/4) | C2 | semidirect |
| 6. #10589399 | C2 | semidirect |
| 7. #10589399 | C2 | semidirect |
| 24. C3×H(3,ℤ/4) | D3 | semidirect |
| 92. H(3,ℤ/4) | C3⋊D3 | semidirect |
| 210. C32 | #2081 | semidirect |
| 251. C3 | #68706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63650 | 2 |
| #10592823 | 2 |
| #10592700 | 2 |
| C32×H(3,ℤ/4) | 2 |
| #10589399 | 2 |
| #68706 | 3 |