Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5183 | C2 | semidirect |
| 4. Dic3×Q16 | C2 | semidirect |
| 8. #4874 | C2 | semidirect |
| 9. #4873 | C2 | semidirect |
| 10. #4792 | C2 | semidirect |
| 11. #4790 | C2 | semidirect |
| 122. C2×Dic3 | Q16 | semidirect |
| 224. C3 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5622 | 2 |
| C3×#467 | 2 |
| #5183 | 2 |
| Dic3×Q16 | 2 |
| #5116 | 2 |
| C2×C8×Dic3 | 2 |
| #5051 | 2 |
| #4874 | 2 |
| #4873 | 2 |
| #4792 | 2 |
| #4790 | 2 |
| #3170 | 3 |