Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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. #5234 | C2 | semidirect |
| 3. #5232 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. C2×#822 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 225. C3 | #2051 | 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 |
| #5234 | 2 |
| #5232 | 2 |
| C2×#833 | 2 |
| C2×#832 | 2 |
| C2×#822 | 2 |
| #4554 | 2 |
| #2051 | 3 |