Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
684 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 425 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 |
|---|---|---|
| 8. C3×C4×Q8 | C4 | semidirect |
| 11. Q8×Dic3 | C4 | direct (N × H) |
| 36. C4×Dic3 | Q8 | direct (N × H) |
| 39. C4×Q8 | Dic3 | direct (N × H) |
| 49. C3×Q8 | C42 | semidirect |
| 84. C3×C4 | C4×Q8 | semidirect |
| 86. Dic3 | C4×Q8 | direct (N × H) |
| 88. Q8 | C4×Dic3 | direct (N × H) |
| 116. C4 | Q8×Dic3 | direct (N × H) |
| 117. C3 | C42×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Q8 | 2 |
| C2×Q8×Dic3 | 2 |
| Dic3×C4⋊C4 | 2 |
| C4×C4⋊Dic3 | 2 |
| C42×Dic3 | 2 |
| C42×Q8 | 3 |