Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#798 | C2 | semidirect |
| 4. C3×#350 | C2 | semidirect |
| 5. #4561 | C2 | semidirect |
| 6. #4515 | C2 | semidirect |
| 7. #4508 | C2 | semidirect |
| 20. C3×M32 | C22 | semidirect |
| 21. C2×C3×C16 | C22 | semidirect |
| 22. #812 | C22 | semidirect |
| 23. C2×C3⋊C16 | C22 | semidirect |
| 34. #350 | D3 | semidirect |
| 83. M32 | C2×D3 | semidirect |
| 86. C2×C16 | C2×D3 | semidirect |
| 210. C3 | #2117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#131 | 2 |
| D3×M32 | 2 |
| C2×#798 | 2 |
| C3×#350 | 2 |
| #4561 | 2 |
| #4515 | 2 |
| #4508 | 2 |
| #2117 | 3 |