Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. C3×#347 | C2 | semidirect |
| 4. #4512 | C2 | semidirect |
| 5. #4466 | C2 | semidirect |
| 16. #798 | C4 | semidirect |
| 17. D3×C16 | C4 | semidirect |
| 22. #347 | D3 | direct (N × H) |
| 36. C3×C16 | C2×C4 | semidirect |
| 37. C3⋊C16 | C2×C4 | semidirect |
| 77. C16 | C4×D3 | semidirect |
| 105. D3 | #347 | direct (N × H) |
| 116. C3 | C2×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×M32 | 2 |
| D3×#97 | 2 |
| C3×#347 | 2 |
| #4512 | 2 |
| #4466 | 2 |
| C2×#347 | 3 |