Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 117 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×#346 | C2 | semidirect |
| 4. #4502 | C2 | semidirect |
| 5. #4461 | C2 | semidirect |
| 16. D3×C16 | C4 | semidirect |
| 21. #346 | D3 | direct (N × H) |
| 33. C3×C16 | C2×C4 | semidirect |
| 34. C3⋊C16 | C2×C4 | semidirect |
| 69. C16 | C4×D3 | semidirect |
| 92. D3 | #346 | direct (N × H) |
| 101. C3 | C2×#346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C16 | 2 |
| C4×D3×C8 | 2 |
| C3×#346 | 2 |
| #4502 | 2 |
| #4461 | 2 |
| C2×#346 | 3 |