Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
461 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 94 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×#5195 | C2 | semidirect |
| 3. C3×#4909 | C2 | semidirect |
| 4. C3×#4867 | C2 | semidirect |
| 5. C32×#360 | C2 | semidirect |
| 6. C3×#4514 | C2 | semidirect |
| 7. C3×#4488 | C2 | semidirect |
| 9. #69253 | C3 | direct (N × H) |
| 17. C2×C3×Dic12 | C22 | semidirect |
| 21. C32×M32 | C22 | semidirect |
| 22. C32×#106 | C22 | semidirect |
| 25. C3×#812 | C22 | semidirect |
| 34. #5195 | C2×C3 | semidirect |
| 35. #4909 | C2×C3 | semidirect |
| 36. #4867 | C2×C3 | semidirect |
| 39. C3×#360 | D3 | semidirect |
| 40. C3×#360 | C2×C3 | semidirect |
| 42. #4514 | C2×C3 | semidirect |
| 43. #4488 | C2×C3 | semidirect |
| 97. C2×Dic12 | C22×C3 | semidirect |
| 107. C3×M32 | C2×D3 | semidirect |
| 108. C3×M32 | C22×C3 | semidirect |
| 110. C3×#106 | C2×D3 | semidirect |
| 111. C3×#106 | C22×C3 | semidirect |
| 115. #812 | C22×C3 | semidirect |
| 152. #360 | C3×D3 | semidirect |
| 256. M32 | C2×C3×D3 | semidirect |
| 257. #106 | C2×C3×D3 | semidirect |
| 393. C32 | #2191 | semidirect |
| 449. C3 | #69253 | direct (N × H) |
| 450. C3 | C3×#2191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5768 | 2 |
| C3×#5195 | 2 |
| C3×#4909 | 2 |
| C3×#4867 | 2 |
| C32×#360 | 2 |
| C3×#4514 | 2 |
| C3×#4488 | 2 |
| C3×#2191 | 3 |
| #69253 | 3 |