Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C3×#536 | C2 | semidirect |
| 3. C2×#947 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. C2×#836 | C2 | semidirect |
| 6. #5001 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 31. #536 | D3 | semidirect |
| 254. C3 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| C2×#949 | 2 |
| C2×#947 | 2 |
| C2×#837 | 2 |
| C2×#836 | 2 |
| #5001 | 2 |
| #4532 | 2 |
| #2003 | 3 |