Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5479 | C2 | semidirect |
| 2. C3×C4×M16 | C2 | semidirect |
| 3. #5137 | C2 | semidirect |
| 5. #5134 | C2 | semidirect |
| 6. #4716 | C2 | semidirect |
| 7. #4711 | C2 | semidirect |
| 8. #4710 | C2 | semidirect |
| 9. #4697 | C2 | semidirect |
| 10. #4696 | C2 | semidirect |
| 11. #4683 | C2 | semidirect |
| 50. C4×M16 | D3 | semidirect |
| 214. C3 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| C3×C4×M16 | 2 |
| #5137 | 2 |
| #5135 | 2 |
| #5134 | 2 |
| #4716 | 2 |
| #4711 | 2 |
| #4710 | 2 |
| #4697 | 2 |
| #4696 | 2 |
| #4683 | 2 |
| #3183 | 3 |