Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 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. #5137 | C2 | semidirect |
| 4. #5121 | C2 | semidirect |
| 5. #4829 | C2 | semidirect |
| 6. #4723 | C2 | semidirect |
| 7. #4722 | C2 | semidirect |
| 8. C4×Dic12 | C2 | semidirect |
| 9. #4683 | C2 | semidirect |
| 188. C3 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5541 | 2 |
| C3×#436 | 2 |
| #5137 | 2 |
| #5121 | 2 |
| #4829 | 2 |
| #4723 | 2 |
| #4722 | 2 |
| C4×Dic12 | 2 |
| #4683 | 2 |
| #3352 | 3 |