Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 35 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×#343 | C2 | semidirect |
| 3. #4528 | C2 | semidirect |
| 13. #343 | D3 | semidirect |
| 138. C3 | #1345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4991 | 2 |
| C3×#343 | 2 |
| #4528 | 2 |
| #1345 | 3 |