Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 36 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×M16 | C2 | semidirect |
| 3. C42×A4 | C2 | semidirect |
| 4. C22×#104 | C3 | semidirect |
| 5. Q8×A4 | C4 | semidirect |
| 7. D4×A4 | C4 | semidirect |
| 14. C22×M16 | C2×C3 | semidirect |
| 15. C22×C42 | C2×C3 | semidirect |
| 35. C22×Q8 | C3×C4 | semidirect |
| 37. C22×D4 | C3×C4 | semidirect |
| 52. #104 | A4 | direct (N × H) |
| 104. M16 | C2×A4 | semidirect |
| 110. C42 | C2×A4 | semidirect |
| 113. A4 | #104 | direct (N × H) |
| 130. Q8 | C4×A4 | semidirect |
| 139. D4 | C4×A4 | semidirect |
| 180. C22 | C3×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#41 | 2 |
| A4×M16 | 2 |
| C42×A4 | 2 |
| C22×#104 | 3 |
| C3×#104 | 4 |