Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
242 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 2. A4×Dic12 | C2 | semidirect |
| 3. A4×C3⋊C16 | C2 | semidirect |
| 4. C22×#827 | C3 | semidirect |
| 11. C22×Dic12 | C2×C3 | semidirect |
| 19. C22×C3⋊C16 | C2×C3 | semidirect |
| 47. #827 | A4 | direct (N × H) |
| 88. Dic12 | C2×A4 | semidirect |
| 91. C3⋊C16 | C2×A4 | semidirect |
| 93. C3×A4 | SD32 | semidirect |
| 173. C22×C3 | C3×SD32 | semidirect |
| 175. A4 | #827 | direct (N × H) |
| 220. C22 | C3×#827 | semidirect |
| 227. C3 | A4×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×D8 | 2 |
| A4×Dic12 | 2 |
| A4×C3⋊C16 | 2 |
| C22×#827 | 3 |
| A4×SD32 | 3 |
| C3×#827 | 4 |