Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
451 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10590327 | C2 | semidirect |
| 3. C3×#4457 | C2 | semidirect |
| 4. C3×#4455 | C2 | semidirect |
| 5. #10589082 | C2 | semidirect |
| 27. #4457 | D3 | semidirect |
| 28. #4455 | D3 | semidirect |
| 36. #3745 | C8 | semidirect |
| 73. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 77. C32×C8 | C2×C8 | semidirect |
| 171. C3×C8 | D3×C8 | semidirect |
| 172. C3×C8 | D3×C8 | semidirect |
| 219. C32 | #1580 | semidirect |
| 233. C8 | #3710 | semidirect |
| 256. C3 | #68077 | semidirect |
| 257. C3 | #68518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| #10590327 | 2 |
| C3×#4457 | 2 |
| C3×#4455 | 2 |
| #10589082 | 2 |
| #68518 | 3 |
| #68077 | 3 |