Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
738 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 210 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×#63773 | C2 | semidirect |
| 3. #10593762 | C2 | direct (N × H) |
| 4. C2×#63765 | C2 | semidirect |
| 5. C2×#63764 | C2 | semidirect |
| 15. #63773 | C22 | semidirect |
| 16. C2×#3708 | C22 | semidirect |
| 17. #63765 | C22 | semidirect |
| 18. #63764 | C22 | semidirect |
| 42. #3708 | C23 | semidirect |
| 108. C2×C3⋊D3 | M32 | semidirect |
| 153. C2×C32 | C2×M32 | semidirect |
| 156. C3⋊D3 | C2×M32 | semidirect |
| 193. C32 | C22×M32 | semidirect |
| 239. C2 | #10593762 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C2×#63773 | 2 |
| #10593762 | 2 |
| C2×#63765 | 2 |
| C2×#63764 | 2 |
| C22×M32 | 9 |