Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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. C3×#421 | C2 | semidirect |
| 3. #5237 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #5125 | C2 | semidirect |
| 6. #5001 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 28. #421 | D3 | semidirect |
| 214. C3 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#949 | 2 |
| C3×#421 | 2 |
| #5237 | 2 |
| C2×#823 | 2 |
| #5125 | 2 |
| #5001 | 2 |
| #4533 | 2 |
| #2048 | 3 |