Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1044 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 169 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×#64160 | C2 | semidirect |
| 3. #10595997 | C2 | semidirect |
| 4. C32×#410 | C2 | semidirect |
| 5. #10592704 | C2 | semidirect |
| 6. #10592703 | C2 | semidirect |
| 7. #10589399 | C2 | semidirect |
| 35. C3×#410 | D3 | semidirect |
| 150. #410 | C3⋊D3 | semidirect |
| 341. C32 | #2009 | semidirect |
| 403. C3 | #70053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64160 | 2 |
| #10596293 | 2 |
| #10595997 | 2 |
| C32×#410 | 2 |
| #10592704 | 2 |
| #10592703 | 2 |
| #10589399 | 2 |
| #70053 | 3 |