Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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×#419 | C2 | semidirect |
| 4. #5225 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 14. #947 | C4 | semidirect |
| 28. #419 | D3 | semidirect |
| 38. C2×C3×Q8 | C2×C4 | semidirect |
| 61. C4×Dic3 | C2×C4 | semidirect |
| 116. C2×Q8 | C4×D3 | semidirect |
| 209. C3 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#947 | 2 |
| #5521 | 2 |
| C3×#419 | 2 |
| #5225 | 2 |
| C2×#823 | 2 |
| #4555 | 2 |
| #4532 | 2 |
| #1885 | 3 |