Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #5681 | C2 | semidirect |
| 2. C3×#495 | C2 | semidirect |
| 3. #5191 | C2 | semidirect |
| 4. Dic3×Q16 | C2 | semidirect |
| 5. #5165 | C2 | semidirect |
| 6. #5163 | C2 | semidirect |
| 8. Dic3×D8 | C2 | semidirect |
| 9. #5057 | C2 | semidirect |
| 10. C4×D24 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 42. #495 | D3 | semidirect |
| 235. C3 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5681 | 2 |
| C3×#495 | 2 |
| #5191 | 2 |
| Dic3×Q16 | 2 |
| #5165 | 2 |
| #5163 | 2 |
| #5151 | 2 |
| Dic3×D8 | 2 |
| #5057 | 2 |
| C4×D24 | 2 |
| C8×Dic6 | 2 |
| #3396 | 3 |