Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 48 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×C4⋊C8 | C3 | semidirect |
| 16. C4×A4 | C8 | semidirect |
| 35. C4⋊C8 | A4 | direct (N × H) |
| 55. C22×C4 | C3×C8 | semidirect |
| 70. A4 | C4⋊C8 | direct (N × H) |
| 118. C22 | C3×C4⋊C8 | semidirect |
| 125. C4 | C8×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×A4 | 2 |
| C42×A4 | 2 |
| C22×C4⋊C8 | 3 |
| C3×C4⋊C8 | 4 |