Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 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×#97 | C2 | semidirect |
| 3. C3×#329 | C2 | semidirect |
| 4. #4540 | C2 | semidirect |
| 5. #4464 | C2 | semidirect |
| 17. C3×#97 | C22 | semidirect |
| 19. #803 | C22 | semidirect |
| 24. #329 | D3 | direct (N × H) |
| 59. #97 | C2×D3 | semidirect |
| 144. D3 | #329 | direct (N × H) |
| 159. C3 | C2×#329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#124 | 2 |
| D3×#97 | 2 |
| C3×#329 | 2 |
| #4540 | 2 |
| #4464 | 2 |
| C2×#329 | 3 |