Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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. #5819 | C2 | semidirect |
| 3. #5236 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. C3⋊#338 | C2 | semidirect |
| 7. #4556 | C2 | semidirect |
| 13. C2×C3×SD16 | C4 | semidirect |
| 14. C2×C3×D8 | C4 | semidirect |
| 72. C2×SD16 | Dic3 | semidirect |
| 73. C2×D8 | Dic3 | semidirect |
| 218. C3 | #1903 | 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 |
| #5819 | 2 |
| #5236 | 2 |
| C2×#833 | 2 |
| #5215 | 2 |
| C3⋊#338 | 2 |
| #4556 | 2 |
| #1903 | 3 |