Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×D3×C16 | C2 | semidirect |
| 3. #4880 | C2 | semidirect |
| 4. C3×#357 | C2 | semidirect |
| 5. #4562 | C2 | semidirect |
| 6. #4503 | C2 | semidirect |
| 7. #4492 | C2 | semidirect |
| 13. #912 | C4 | semidirect |
| 29. #357 | D3 | semidirect |
| 155. C3 | #2138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#912 | 2 |
| C2×D3×C16 | 2 |
| #4880 | 2 |
| C3×#357 | 2 |
| #4562 | 2 |
| #4503 | 2 |
| #4492 | 2 |
| #2138 | 3 |