Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
535 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#4694 | C2 | semidirect |
| 3. #10590363 | C2 | semidirect |
| 4. #10590307 | C2 | semidirect |
| 5. #10589322 | C2 | semidirect |
| 6. C3×#4459 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 34. #4694 | D3 | semidirect |
| 38. #4459 | D3 | semidirect |
| 113. #634 | SD16 | semidirect |
| 365. C32 | #1642 | semidirect |
| 424. C3 | #68197 | semidirect |
| 425. C3 | #71199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593906 | 2 |
| C3×#4694 | 2 |
| #10590363 | 2 |
| #10590307 | 2 |
| #10589322 | 2 |
| C3×#4459 | 2 |
| #10589090 | 2 |
| #71199 | 3 |
| #68197 | 3 |