Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. D3×Q32 | C2 | semidirect |
| 3. C3×SD64 | C2 | semidirect |
| 4. #4522 | C2 | semidirect |
| 5. #4520 | C2 | semidirect |
| 6. Dic48 | C2 | semidirect |
| 7. #4447 | C2 | semidirect |
| 25. SD64 | D3 | semidirect |
| 99. C3 | #2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q32 | 2 |
| #4912 | 2 |
| C3×SD64 | 2 |
| #4522 | 2 |
| #4520 | 2 |
| Dic48 | 2 |
| #4447 | 2 |
| #2264 | 3 |