Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
250 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 39 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. A4×D24 | C2 | semidirect |
| 2. C3×A4×C16 | C2 | semidirect |
| 3. C22×D48 | C3 | semidirect |
| 8. C22×D24 | C2×C3 | semidirect |
| 10. C22×C3×C16 | C2×C3 | semidirect |
| 15. A4×C16 | D3 | semidirect |
| 35. D48 | A4 | direct (N × H) |
| 44. C22×C16 | C3×D3 | semidirect |
| 59. D24 | C2×A4 | semidirect |
| 63. C3×C16 | C2×A4 | semidirect |
| 65. C3×A4 | D16 | semidirect |
| 111. C16 | D3×A4 | semidirect |
| 115. C22×C3 | C3×D16 | semidirect |
| 123. A4 | D48 | direct (N × H) |
| 158. C22 | C3×D48 | semidirect |
| 163. C3 | A4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×D24 | 2 |
| C3×A4×C16 | 2 |
| C22×D48 | 3 |
| A4×D16 | 3 |
| C3×D48 | 4 |