Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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. #4833 | C2 | semidirect |
| 3. #4685 | C2 | semidirect |
| 4. C3×D4⋊C8 | C2 | semidirect |
| 5. D4⋊(C3⋊C8) | C2 | semidirect |
| 6. #4483 | C2 | semidirect |
| 7. #4459 | C2 | semidirect |
| 20. C3×C4⋊C8 | C22 | semidirect |
| 21. C3×C4×C8 | C22 | semidirect |
| 26. C4⋊(C3⋊C8) | C22 | semidirect |
| 27. C4×C3⋊C8 | C22 | semidirect |
| 34. D4⋊C8 | D3 | semidirect |
| 41. D3×D4 | C8 | semidirect |
| 79. C4⋊C8 | C2×D3 | semidirect |
| 84. C4×C8 | C2×D3 | semidirect |
| 234. C3 | #1478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×D4 | 2 |
| #4833 | 2 |
| #4685 | 2 |
| C3×D4⋊C8 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4483 | 2 |
| #4459 | 2 |
| #1478 | 3 |