Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 65 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. #4679 | C2 | semidirect |
| 5. #4484 | C2 | semidirect |
| 6. #4479 | C2 | semidirect |
| 7. #4454 | C2 | semidirect |
| 150. C3 | #1585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D4 | 2 |
| C4×#214 | 2 |
| #4679 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4484 | 2 |
| #4479 | 2 |
| #4454 | 2 |
| #1585 | 3 |