Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C2×#810 | C2 | semidirect |
| 5. #4929 | C2 | semidirect |
| 6. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 104. C2×C3×C4 | SD16 | semidirect |
| 210. C2×C4 | #214 | semidirect |
| 250. C3 | #2055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#214 | 2 |
| C3×#390 | 2 |
| C2×#832 | 2 |
| C2×#810 | 2 |
| #4929 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4529 | 2 |
| #2055 | 3 |