Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C23×C3×C8 | C2 | semidirect |
| 3. C2×#926 | C2 | semidirect |
| 4. #5113 | C2 | direct (N × H) |
| 5. C2×#821 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 12. C2×#235 | C4 | semidirect |
| 19. C22×C3×C8 | C22 | semidirect |
| 22. #926 | C22 | semidirect |
| 25. #821 | C22 | semidirect |
| 26. #816 | C22 | semidirect |
| 28. C23×C8 | D3 | semidirect |
| 47. #235 | C2×C4 | semidirect |
| 76. C22×C8 | C2×D3 | semidirect |
| 190. C2×C3 | #416 | semidirect |
| 209. C3 | C2×#416 | semidirect |
| 212. C2 | #5113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C23×C3×C8 | 2 |
| C2×#926 | 2 |
| #5113 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| C2×#416 | 3 |