Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
272 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 64 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×A4×Q16 | C2 | semidirect |
| 3. C3×A4×C16 | C2 | semidirect |
| 4. C22×C3×SD32 | C3 | semidirect |
| 5. A4×SD32 | C3 | direct (N × H) |
| 10. C22×C3×Q16 | C2×C3 | semidirect |
| 12. A4×Q16 | C2×C3 | semidirect |
| 18. C22×C3×C16 | C2×C3 | semidirect |
| 19. A4×C16 | C2×C3 | semidirect |
| 26. C22×SD32 | C32 | semidirect |
| 44. C3×SD32 | A4 | direct (N × H) |
| 52. C22×Q16 | C2×C32 | semidirect |
| 58. C22×C16 | C2×C32 | semidirect |
| 75. C3×Q16 | C2×A4 | semidirect |
| 85. C3×C16 | C2×A4 | semidirect |
| 87. C3×A4 | SD32 | direct (N × H) |
| 103. SD32 | C3×A4 | direct (N × H) |
| 144. Q16 | C2×C3×A4 | semidirect |
| 152. C16 | C2×C3×A4 | semidirect |
| 162. C22×C3 | C3×SD32 | semidirect |
| 163. A4 | C3×SD32 | direct (N × H) |
| 205. C22 | C32×SD32 | semidirect |
| 211. C3 | A4×SD32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×Q16 | 2 |
| C3×A4×D8 | 2 |
| C3×A4×C16 | 2 |
| C22×C3×SD32 | 3 |
| A4×SD32 | 3 |
| C32×SD32 | 4 |