Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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. #5125 | C2 | semidirect |
| 3. C3×#349 | C2 | semidirect |
| 4. #4516 | C2 | semidirect |
| 5. #4513 | C2 | semidirect |
| 20. #349 | D3 | semidirect |
| 106. C3 | #2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5135 | 2 |
| #5125 | 2 |
| C3×#349 | 2 |
| #4516 | 2 |
| #4513 | 2 |
| #2238 | 3 |