Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
822 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 3. #10592634 | C2 | semidirect |
| 4. C32×#336 | C2 | semidirect |
| 5. #10589417 | C2 | semidirect |
| 20. C3×#336 | D3 | semidirect |
| 85. #336 | C3⋊D3 | semidirect |
| 213. C32 | #2071 | semidirect |
| 269. C3 | #68635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63648 | 2 |
| #10592638 | 2 |
| #10592634 | 2 |
| C32×#336 | 2 |
| #10589417 | 2 |
| #68635 | 3 |