Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
798 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 155 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×#413 | C2 | semidirect |
| 3. C2×#63664 | C2 | semidirect |
| 4. C2×#63652 | C2 | semidirect |
| 5. #10592831 | C2 | semidirect |
| 6. #10592817 | C2 | semidirect |
| 7. #10589426 | C2 | semidirect |
| 31. C3×#413 | D3 | semidirect |
| 135. #413 | C3⋊D3 | semidirect |
| 304. C32 | #2050 | semidirect |
| 361. C3 | #70144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596293 | 2 |
| C32×#413 | 2 |
| C2×#63664 | 2 |
| C2×#63652 | 2 |
| #10592831 | 2 |
| #10592817 | 2 |
| #10589426 | 2 |
| #70144 | 3 |