Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
768 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×C32×C4⋊C8 | C2 | semidirect |
| 3. #10592624 | C2 | semidirect |
| 4. #10589351 | C2 | semidirect |
| 5. #10589348 | C2 | semidirect |
| 23. C2×C3×C4⋊C8 | D3 | semidirect |
| 90. C2×C4⋊C8 | C3⋊D3 | semidirect |
| 210. C32 | #1540 | semidirect |
| 254. C3 | #70431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C2×C32×C4⋊C8 | 2 |
| #10592624 | 2 |
| #10589351 | 2 |
| #10589348 | 2 |
| #70431 | 3 |