Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
320 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 96 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×#108 | C3 | semidirect |
| 4. A4×#108 | C3 | direct (N × H) |
| 21. C22×#108 | C32 | semidirect |
| 38. C3×#108 | A4 | direct (N × H) |
| 74. C3×A4 | #108 | direct (N × H) |
| 89. #108 | C3×A4 | direct (N × H) |
| 142. C22×C3 | C3×#108 | semidirect |
| 144. A4 | C3×#108 | direct (N × H) |
| 184. C22 | C32×#108 | semidirect |
| 191. C3 | A4×#108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×M16 | 2 |
| C2×C3×C8×A4 | 2 |
| C22×C3×#108 | 3 |
| A4×#108 | 3 |
| C32×#108 | 4 |