Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. C32×#364 | C2 | semidirect |
| 4. #10589378 | C2 | semidirect |
| 5. #10589329 | C2 | semidirect |
| 17. C3×#364 | D3 | semidirect |
| 60. #364 | C3⋊D3 | semidirect |
| 132. C32 | #2165 | semidirect |
| 157. C3 | #69298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3743 | 2 |
| C32×#364 | 2 |
| #10589380 | 2 |
| #10589378 | 2 |
| #10589329 | 2 |
| #69298 | 3 |