Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5584 | C2 | semidirect |
| 2. C3×#460 | C2 | semidirect |
| 4. #5070 | C2 | semidirect |
| 5. #4535 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 7. #4483 | C2 | semidirect |
| 28. #460 | D3 | semidirect |
| 185. C3 | #1628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5584 | 2 |
| C3×#460 | 2 |
| #5072 | 2 |
| #5070 | 2 |
| #4535 | 2 |
| #4486 | 2 |
| #4483 | 2 |
| #1628 | 3 |