Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
463 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 463 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. C2×C3×#827 | C2 | semidirect |
| 3. C3×#4909 | C2 | semidirect |
| 4. C3×#4896 | C2 | semidirect |
| 5. C32×#361 | C2 | semidirect |
| 6. C3×#4515 | C2 | semidirect |
| 7. C3×#4497 | C2 | semidirect |
| 9. #69259 | C3 | direct (N × H) |
| 17. C2×C3×Dic12 | C22 | semidirect |
| 20. C32×M32 | C22 | semidirect |
| 21. C32×#108 | C22 | semidirect |
| 24. C2×C3×C3⋊C16 | C22 | semidirect |
| 32. C2×#827 | C2×C3 | semidirect |
| 33. #4909 | C2×C3 | semidirect |
| 34. #4896 | C2×C3 | semidirect |
| 36. C3×#361 | D3 | semidirect |
| 37. C3×#361 | C2×C3 | semidirect |
| 40. #4515 | C2×C3 | semidirect |
| 41. #4497 | C2×C3 | semidirect |
| 88. C2×Dic12 | C22×C3 | semidirect |
| 95. C3×M32 | C2×D3 | semidirect |
| 96. C3×M32 | C22×C3 | semidirect |
| 99. C3×#108 | C2×D3 | semidirect |
| 100. C3×#108 | C22×C3 | semidirect |
| 104. C2×C3⋊C16 | C22×C3 | semidirect |
| 134. #361 | C3×D3 | semidirect |
| 221. M32 | C2×C3×D3 | semidirect |
| 223. #108 | C2×C3×D3 | semidirect |
| 337. C32 | #2194 | semidirect |
| 386. C3 | #69259 | direct (N × H) |
| 387. C3 | C3×#2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5757 | 2 |
| C2×C3×#827 | 2 |
| C3×#4909 | 2 |
| C3×#4896 | 2 |
| C32×#361 | 2 |
| C3×#4515 | 2 |
| C3×#4497 | 2 |
| C3×#2194 | 3 |
| #69259 | 3 |