Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
440 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 90 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×C4⋊C4 | C2 | semidirect |
| 4. C42×A4 | C2 | semidirect |
| 5. C22×#117 | C3 | semidirect |
| 7. C2×C4×A4 | C4 | semidirect |
| 18. C22×C4⋊C4 | C2×C3 | semidirect |
| 20. C22×C42 | C2×C3 | semidirect |
| 37. C23×C4 | C3×C4 | semidirect |
| 49. #117 | A4 | direct (N × H) |
| 102. C4⋊C4 | C2×A4 | semidirect |
| 110. C42 | C2×A4 | semidirect |
| 114. A4 | #117 | direct (N × H) |
| 156. C2×C4 | C4×A4 | semidirect |
| 179. C22 | C3×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×A4 | 2 |
| A4×C4⋊C4 | 2 |
| A4×C22⋊C4 | 2 |
| C42×A4 | 2 |
| C22×#117 | 3 |
| C3×#117 | 4 |