Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C3×#5752 | C2 | semidirect |
| 2. C3×#5142 | C2 | semidirect |
| 3. C3×#4908 | C2 | semidirect |
| 4. C2×C3×D48 | C2 | semidirect |
| 5. C32×#350 | C2 | semidirect |
| 6. C3×#4516 | C2 | semidirect |
| 7. C3×#4510 | C2 | semidirect |
| 9. #69126 | C3 | direct (N × H) |
| 19. C2×C3×D24 | C22 | semidirect |
| 20. C32×M32 | C22 | semidirect |
| 21. C2×C32×C16 | C22 | semidirect |
| 23. C3×#819 | C22 | semidirect |
| 28. #5752 | C2×C3 | semidirect |
| 32. #5142 | C2×C3 | semidirect |
| 33. #4908 | C2×C3 | semidirect |
| 34. C2×D48 | C2×C3 | semidirect |
| 38. C3×#350 | D3 | semidirect |
| 39. C3×#350 | C2×C3 | semidirect |
| 40. #4516 | C2×C3 | semidirect |
| 41. #4510 | C2×C3 | semidirect |
| 90. C2×D24 | C22×C3 | semidirect |
| 95. C3×M32 | C2×D3 | semidirect |
| 96. C3×M32 | C22×C3 | semidirect |
| 98. C2×C3×C16 | C2×D3 | semidirect |
| 99. C2×C3×C16 | C22×C3 | semidirect |
| 103. #819 | C22×C3 | semidirect |
| 136. #350 | C3×D3 | semidirect |
| 223. M32 | C2×C3×D3 | semidirect |
| 224. C2×C16 | C2×C3×D3 | semidirect |
| 343. C32 | #2192 | semidirect |
| 395. C3 | #69126 | direct (N × H) |
| 396. C3 | C3×#2192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5752 | 2 |
| C3×#5142 | 2 |
| C3×#4908 | 2 |
| C2×C3×D48 | 2 |
| C32×#350 | 2 |
| C3×#4516 | 2 |
| C3×#4510 | 2 |
| C3×#2192 | 3 |
| #69126 | 3 |