Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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×#343 | C2 | semidirect |
| 4. #4554 | C2 | semidirect |
| 5. #4530 | C2 | semidirect |
| 15. D3×M16 | C4 | semidirect |
| 24. #343 | D3 | direct (N × H) |
| 39. C3×M16 | C2×C4 | semidirect |
| 45. #208 | C2×C4 | semidirect |
| 105. M16 | C4×D3 | semidirect |
| 162. D3 | #343 | direct (N × H) |
| 181. C3 | C2×#343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C3×#343 | 2 |
| #4554 | 2 |
| #4530 | 2 |
| C2×#343 | 3 |