Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
110 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 24 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×Q16 | C2 | semidirect |
| 3. A4×C16 | C2 | semidirect |
| 4. C22×SD32 | C3 | semidirect |
| 9. C22×Q16 | C2×C3 | semidirect |
| 15. C22×C16 | C2×C3 | semidirect |
| 35. SD32 | A4 | direct (N × H) |
| 55. Q16 | C2×A4 | semidirect |
| 63. C16 | C2×A4 | semidirect |
| 65. A4 | SD32 | direct (N × H) |
| 97. C22 | C3×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×Q16 | 2 |
| A4×D8 | 2 |
| A4×C16 | 2 |
| C22×SD32 | 3 |
| C3×SD32 | 4 |