Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. D3×M32 | C2 | semidirect |
| 3. D3×#108 | C2 | semidirect |
| 4. C3×#361 | C2 | semidirect |
| 5. #4563 | C2 | semidirect |
| 6. #4516 | C2 | semidirect |
| 7. #4495 | C2 | semidirect |
| 19. C3×M32 | C22 | semidirect |
| 20. C3×#108 | C22 | semidirect |
| 22. #819 | C22 | semidirect |
| 23. #812 | C22 | semidirect |
| 32. #361 | D3 | direct (N × H) |
| 72. M32 | C2×D3 | semidirect |
| 76. #108 | C2×D3 | semidirect |
| 171. D3 | #361 | direct (N × H) |
| 186. C3 | C2×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D8 | 2 |
| D3×M32 | 2 |
| D3×#108 | 2 |
| C3×#361 | 2 |
| #4563 | 2 |
| #4516 | 2 |
| #4495 | 2 |
| C2×#361 | 3 |