Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4919 | C2 | semidirect |
| 2. C3×D3×D16 | C2 | semidirect |
| 3. C32×SD64 | C2 | semidirect |
| 4. C3×#4521 | C2 | semidirect |
| 5. C3×#4519 | C2 | semidirect |
| 6. C3×D96 | C2 | semidirect |
| 7. C3×#4447 | C2 | semidirect |
| 9. #69380 | C3 | direct (N × H) |
| 12. C32×Q32 | C22 | semidirect |
| 17. C3×D48 | C22 | semidirect |
| 19. C32×C32 | C22 | semidirect |
| 20. C3×C3⋊C32 | C22 | semidirect |
| 23. #4919 | C2×C3 | semidirect |
| 24. D3×D16 | C2×C3 | semidirect |
| 27. C3×SD64 | D3 | semidirect |
| 28. C3×SD64 | C2×C3 | semidirect |
| 32. #4521 | C2×C3 | semidirect |
| 33. #4519 | C2×C3 | semidirect |
| 34. D96 | C2×C3 | semidirect |
| 35. #4447 | C2×C3 | semidirect |
| 53. C3×Q32 | C2×D3 | semidirect |
| 54. C3×Q32 | C22×C3 | semidirect |
| 66. D48 | C22×C3 | semidirect |
| 70. C3×C32 | C2×D3 | semidirect |
| 71. C3×C32 | C22×C3 | semidirect |
| 72. C3⋊C32 | C22×C3 | semidirect |
| 87. SD64 | C3×D3 | semidirect |
| 126. Q32 | C2×C3×D3 | semidirect |
| 134. C32 | C2×C3×D3 | semidirect |
| 195. C32 | #2263 | semidirect |
| 228. C3 | #69380 | direct (N × H) |
| 229. C3 | C3×#2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4919 | 2 |
| C3×D3×D16 | 2 |
| C32×SD64 | 2 |
| C3×#4521 | 2 |
| C3×#4519 | 2 |
| C3×D96 | 2 |
| C3×#4447 | 2 |
| C3×#2263 | 3 |
| #69380 | 3 |