Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. #5825 | C2 | semidirect |
| 3. C2×#936 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. C2×#824 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 254. C3 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| #5825 | 2 |
| C2×#936 | 2 |
| C2×#837 | 2 |
| #5215 | 2 |
| C2×#824 | 2 |
| #4555 | 2 |
| #2003 | 3 |