Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10590818 | C2 | semidirect |
| 4. C2×#63550 | C2 | semidirect |
| 5. #10589367 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 33. #4503 | D3 | semidirect |
| 269. C32 | #2211 | semidirect |
| 309. C3 | #69237 | semidirect |
| 310. C3 | #71478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#800 | 2 |
| #10590869 | 2 |
| #10590818 | 2 |
| C2×#63550 | 2 |
| #10589367 | 2 |
| C3×#4503 | 2 |
| #10589114 | 2 |
| #71478 | 3 |
| #69237 | 3 |