Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. C3×#491 | C2 | semidirect |
| 4. #5082 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 7. #4792 | C2 | semidirect |
| 9. #4703 | C2 | semidirect |
| 37. #491 | D3 | semidirect |
| 171. C3 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| #5688 | 2 |
| C3×#491 | 2 |
| #5082 | 2 |
| #5069 | 2 |
| #4802 | 2 |
| #4792 | 2 |
| #4707 | 2 |
| #4703 | 2 |
| #3139 | 3 |