Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#948 | C2 | semidirect |
| 3. #5232 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. #4558 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 12. C3×AGL(1,ℤ/8) | C4 | semidirect |
| 75. AGL(1,ℤ/8) | Dic3 | semidirect |
| 239. C3 | #1907 | 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 |
| C2×#948 | 2 |
| #5232 | 2 |
| C2×#833 | 2 |
| C2×#832 | 2 |
| #4558 | 2 |
| #4554 | 2 |
| #1907 | 3 |