Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
499 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 499 conjugacy classes of subgroups — too many to draw. Only its 92 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. C4⋊SL(2,ℤ/4) | C2 | direct (N × H) |
| 6. C2×C4×A4 | C4 | semidirect |
| 24. C4×A4 | C2×C4 | semidirect |
| 34. C23×C4 | Dic3 | semidirect |
| 48. C2×A4 | C4⋊C4 | semidirect |
| 86. C22×C4 | C2×Dic3 | semidirect |
| 98. A4 | C2×C4⋊C4 | semidirect |
| 122. C23 | C4⋊Dic3 | semidirect |
| 144. C2×C4 | SL(2,ℤ/4) | semidirect |
| 171. C22 | C2×C4⋊Dic3 | semidirect |
| 179. C4 | C2×SL(2,ℤ/4) | semidirect |
| 186. C2 | C4⋊SL(2,ℤ/4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×A4 | 2 |
| C22×SL(2,ℤ/4) | 2 |
| C4⋊SL(2,ℤ/4) | 2 |
| C2×#380 | 3 |
| C2×C4⋊Dic3 | 4 |