Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
832 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 224 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. C3×A4×M16 | C2 | semidirect |
| 3. C2×C3×C8×A4 | C2 | semidirect |
| 4. C22×C3×#131 | C3 | semidirect |
| 5. A4×#131 | C3 | direct (N × H) |
| 18. C22×C3×M16 | C2×C3 | semidirect |
| 19. C23×C3×C8 | C2×C3 | semidirect |
| 20. A4×M16 | C2×C3 | semidirect |
| 21. C2×C8×A4 | C2×C3 | semidirect |
| 28. C22×#131 | C32 | semidirect |
| 46. C3×#131 | A4 | direct (N × H) |
| 70. C22×M16 | C2×C32 | semidirect |
| 71. C23×C8 | C2×C32 | semidirect |
| 99. C3×M16 | C2×A4 | semidirect |
| 109. C2×C3×C8 | C2×A4 | semidirect |
| 111. C3×A4 | #131 | direct (N × H) |
| 127. #131 | C3×A4 | direct (N × H) |
| 193. M16 | C2×C3×A4 | semidirect |
| 202. C2×C8 | C2×C3×A4 | semidirect |
| 211. C22×C3 | C3×#131 | semidirect |
| 213. A4 | C3×#131 | direct (N × H) |
| 260. C22 | C32×#131 | semidirect |
| 267. C3 | A4×#131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×#41 | 2 |
| C3×A4×M16 | 2 |
| C2×C3×C8×A4 | 2 |
| C22×C3×#131 | 3 |
| A4×#131 | 3 |
| C32×#131 | 4 |