Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×C32×SD32 | C2 | semidirect |
| 2. #10592891 | C2 | semidirect |
| 4. #10592600 | C2 | semidirect |
| 5. #10589431 | C2 | semidirect |
| 6. #10589429 | C2 | semidirect |
| 7. #10589372 | C2 | semidirect |
| 24. C2×C3×SD32 | D3 | semidirect |
| 83. C2×SD32 | C3⋊D3 | semidirect |
| 181. C32 | #2223 | semidirect |
| 210. C3 | #71491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD32 | 2 |
| #10592891 | 2 |
| #10592859 | 2 |
| #10592600 | 2 |
| #10589431 | 2 |
| #10589429 | 2 |
| #10589372 | 2 |
| #71491 | 3 |