Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1200 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 321 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. C32×#533 | C2 | semidirect |
| 3. #10592792 | C2 | semidirect |
| 4. #10592787 | C2 | semidirect |
| 5. #10592767 | C2 | semidirect |
| 6. #10592701 | C2 | semidirect |
| 7. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 26. C3×#533 | D3 | semidirect |
| 89. #533 | C3⋊D3 | semidirect |
| 198. C32 | #3131 | semidirect |
| 231. C3 | #83334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#533 | 2 |
| #10595948 | 2 |
| #10592792 | 2 |
| #10592787 | 2 |
| #10592767 | 2 |
| #10592701 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #83334 | 3 |