Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 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 |
|---|---|---|
| 2. C3×#347 | C2 | semidirect |
| 4. #4511 | C2 | semidirect |
| 5. #4466 | C2 | semidirect |
| 20. #347 | D3 | semidirect |
| 97. C3 | #2166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4708 | 2 |
| C3×#347 | 2 |
| #4514 | 2 |
| #4511 | 2 |
| #4466 | 2 |
| #2166 | 3 |