Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
846 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#63650 | C2 | semidirect |
| 3. #10592828 | C2 | semidirect |
| 4. C2×#63649 | C2 | semidirect |
| 5. #10592665 | C2 | semidirect |
| 6. C2×#63636 | C2 | semidirect |
| 7. C32×#343 | C2 | semidirect |
| 32. C3×#343 | D3 | semidirect |
| 122. #343 | C3⋊D3 | semidirect |
| 283. C32 | #2051 | semidirect |
| 342. C3 | #68986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64117 | 2 |
| C2×#63650 | 2 |
| #10592828 | 2 |
| C2×#63649 | 2 |
| #10592665 | 2 |
| C2×#63636 | 2 |
| C32×#343 | 2 |
| #68986 | 3 |