Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C32×#362 | C2 | semidirect |
| 5. #10589431 | C2 | semidirect |
| 6. #10589383 | C2 | semidirect |
| 7. #10589362 | C2 | semidirect |
| 29. C3×#362 | D3 | semidirect |
| 107. #362 | C3⋊D3 | direct (N × H) |
| 188. C3⋊D3 | #362 | direct (N × H) |
| 226. C32 | C2×#362 | semidirect |
| 264. C3 | D3×#362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| C3⋊D3×M32 | 2 |
| C3⋊D3×#108 | 2 |
| C32×#362 | 2 |
| #10589431 | 2 |
| #10589383 | 2 |
| #10589362 | 2 |
| D3×#362 | 3 |