Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 66 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×Q16 | C2 | direct (N × H) |
| 4. C23×Q16 | C3 | semidirect |
| 16. C22×Q16 | C2×C3 | semidirect |
| 43. C2×Q16 | A4 | direct (N × H) |
| 48. C2×A4 | Q16 | direct (N × H) |
| 84. Q16 | C2×A4 | direct (N × H) |
| 92. A4 | C2×Q16 | direct (N × H) |
| 99. C23 | C3×Q16 | semidirect |
| 135. C22 | C2×C3×Q16 | semidirect |
| 147. C2 | A4×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×A4 | 2 |
| A4×Q16 | 2 |
| C2×C8×A4 | 2 |
| C23×Q16 | 3 |
| C2×C3×Q16 | 4 |