Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
557 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 557 conjugacy classes of subgroups — too many to draw. Only its 92 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×#63654 | C2 | semidirect |
| 3. #10590852 | C2 | semidirect |
| 4. C2×#63548 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 12. C2×#3746 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 21. C3×#818 | C22 | semidirect |
| 22. C2×C3×C3⋊C16 | C22 | semidirect |
| 36. #4562 | D3 | semidirect |
| 91. #818 | C2×D3 | semidirect |
| 96. C2×C3⋊C16 | C2×D3 | semidirect |
| 194. C2×C3×D3 | SD32 | semidirect |
| 323. C2×D3 | #827 | semidirect |
| 337. C32 | #2187 | semidirect |
| 393. C3 | #69193 | semidirect |
| 394. C3 | #72036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×D8 | 2 |
| C2×#63654 | 2 |
| #10590852 | 2 |
| C2×#63548 | 2 |
| C3×#4562 | 2 |
| #10589114 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #72036 | 3 |
| #69193 | 3 |