Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 473 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. C32×#510 | C2 | semidirect |
| 3. C3×#5189 | C2 | semidirect |
| 4. C3×#5179 | C2 | semidirect |
| 5. C3×#4566 | C2 | semidirect |
| 6. C3×#4518 | C2 | semidirect |
| 7. C3×#4514 | C2 | semidirect |
| 9. #71522 | C3 | direct (N × H) |
| 12. C2×C32×Q16 | C22 | semidirect |
| 23. C32×M32 | C22 | semidirect |
| 27. C3×#817 | C22 | semidirect |
| 28. C3×#812 | C22 | semidirect |
| 33. C3×#510 | D3 | semidirect |
| 34. C3×#510 | C2×C3 | semidirect |
| 36. #5189 | C2×C3 | semidirect |
| 37. #5179 | C2×C3 | semidirect |
| 41. #4566 | C2×C3 | semidirect |
| 42. #4518 | C2×C3 | semidirect |
| 43. #4514 | C2×C3 | semidirect |
| 90. C2×C3×Q16 | C2×D3 | semidirect |
| 91. C2×C3×Q16 | C22×C3 | semidirect |
| 112. C3×M32 | C2×D3 | semidirect |
| 113. C3×M32 | C22×C3 | semidirect |
| 119. #817 | C22×C3 | semidirect |
| 120. #812 | C22×C3 | semidirect |
| 151. #510 | C3×D3 | semidirect |
| 252. C2×Q16 | C2×C3×D3 | semidirect |
| 260. M32 | C2×C3×D3 | semidirect |
| 399. C32 | #2191 | semidirect |
| 455. C3 | #71522 | direct (N × H) |
| 456. 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 |
| C32×#510 | 2 |
| C3×#5189 | 2 |
| C3×#5179 | 2 |
| C3×#4566 | 2 |
| C3×#4518 | 2 |
| C3×#4514 | 2 |
| C3×#2191 | 3 |
| #71522 | 3 |