Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
786 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 193 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×C4×M16 | C2 | semidirect |
| 3. #10592624 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 22. C3×C4×M16 | D3 | semidirect |
| 84. C4×M16 | C3⋊D3 | semidirect |
| 196. C32 | #1484 | semidirect |
| 236. C3 | #69853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C32×C4×M16 | 2 |
| #10592624 | 2 |
| #10589325 | 2 |
| #69853 | 3 |