Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
618 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 117 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×#473 | C2 | semidirect |
| 3. C2×#63656 | C2 | semidirect |
| 4. #10592878 | C2 | semidirect |
| 5. #10589427 | C2 | semidirect |
| 6. #10589363 | C2 | semidirect |
| 7. #10589362 | C2 | semidirect |
| 27. C3×#473 | D3 | semidirect |
| 104. #473 | C3⋊D3 | semidirect |
| 224. C32 | #2195 | semidirect |
| 261. C3 | #71099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596224 | 2 |
| C32×#473 | 2 |
| C2×#63656 | 2 |
| #10592878 | 2 |
| #10589427 | 2 |
| #10589363 | 2 |
| #10589362 | 2 |
| #71099 | 3 |