Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
322 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 322 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. #4726 | C2 | semidirect |
| 3. D3×C22⋊C8 | C2 | semidirect |
| 4. C3×#323 | C2 | semidirect |
| 5. #4525 | C2 | semidirect |
| 6. #4468 | C2 | semidirect |
| 7. #4468 | C2 | semidirect |
| 34. #323 | D3 | semidirect |
| 269. C3 | #1471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#884 | 2 |
| #4726 | 2 |
| D3×C22⋊C8 | 2 |
| C3×#323 | 2 |
| #4525 | 2 |
| #4468 | 2 |
| #1471 | 3 |