Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 221 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 | semidirect |
| 5. Dic3×Q16 | C2 | semidirect |
| 10. C2×C3×Q16 | C4 | semidirect |
| 54. C2×Q16 | Dic3 | semidirect |
| 141. C3 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| #5812 | 2 |
| #5225 | 2 |
| #5184 | 2 |
| Dic3×Q16 | 2 |
| #5106 | 2 |
| #5101 | 2 |
| #2950 | 3 |