Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
488 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 3. C22×C3×C4×C8 | C3 | semidirect |
| 4. C4×C8×A4 | C3 | direct (N × H) |
| 7. C3×C8×A4 | C4 | direct (N × H) |
| 17. C3×C4×A4 | C8 | direct (N × H) |
| 21. C22×C4×C8 | C32 | semidirect |
| 29. C22×C3×C8 | C3×C4 | semidirect |
| 33. C8×A4 | C3×C4 | direct (N × H) |
| 38. C3×C4×C8 | A4 | direct (N × H) |
| 57. C22×C3×C4 | C3×C8 | semidirect |
| 59. C4×A4 | C3×C8 | direct (N × H) |
| 74. C3×A4 | C4×C8 | direct (N × H) |
| 82. C22×C8 | C32×C4 | semidirect |
| 89. C4×C8 | C3×A4 | direct (N × H) |
| 113. C3×C8 | C4×A4 | direct (N × H) |
| 123. C22×C4 | C32×C8 | semidirect |
| 143. C22×C3 | C3×C4×C8 | semidirect |
| 145. A4 | C3×C4×C8 | direct (N × H) |
| 150. C3×C4 | C8×A4 | direct (N × H) |
| 171. C8 | C3×C4×A4 | direct (N × H) |
| 186. C22 | C32×C4×C8 | semidirect |
| 190. C4 | C3×C8×A4 | direct (N × H) |
| 193. C3 | C4×C8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×A4 | 2 |
| C3×C42×A4 | 2 |
| C22×C3×C4×C8 | 3 |
| C4×C8×A4 | 3 |
| C32×C4×C8 | 4 |