Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 4. #5184 | C2 | direct (N × H) |
| 9. C2×C3×Q16 | C4 | semidirect |
| 36. C3×Q16 | C2×C4 | semidirect |
| 48. C2×Q16 | Dic3 | semidirect |
| 85. Q16 | C2×Dic3 | semidirect |
| 121. C2×C3 | #441 | semidirect |
| 133. C3 | C2×#441 | semidirect |
| 134. C2 | #5184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×Q8×Dic3 | 2 |
| C2×#835 | 2 |
| #5184 | 2 |
| C2×#817 | 2 |
| C2×#815 | 2 |
| C2×#441 | 3 |