Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
216 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 87 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×C32 | C2 | semidirect |
| 3. #10589365 | C2 | semidirect |
| 13. C2×C3×C32 | D3 | semidirect |
| 41. C2×C32 | C3⋊D3 | semidirect |
| 86. C32 | #1401 | semidirect |
| 103. C3 | #67595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592600 | 2 |
| C2×C32×C32 | 2 |
| #10589365 | 2 |
| #67595 | 3 |