Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 344 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. D3×C4⋊C8 | C2 | semidirect |
| 3. C4×D3×C8 | C2 | semidirect |
| 4. C3×D4⋊C8 | C2 | semidirect |
| 5. D4⋊(C3⋊C8) | C2 | semidirect |
| 6. #4483 | C2 | semidirect |
| 7. #4459 | C2 | semidirect |
| 22. C3×C4⋊C8 | C22 | semidirect |
| 23. C3×C4×C8 | C22 | semidirect |
| 26. C4⋊(C3⋊C8) | C22 | semidirect |
| 27. C4×C3⋊C8 | C22 | semidirect |
| 34. D4⋊C8 | D3 | direct (N × H) |
| 41. D3×D4 | C8 | semidirect |
| 83. C4⋊C8 | C2×D3 | semidirect |
| 86. C4×C8 | C2×D3 | semidirect |
| 94. C3×D4 | C2×C8 | semidirect |
| 108. D12 | C2×C8 | semidirect |
| 186. D4 | D3×C8 | semidirect |
| 216. D3 | D4⋊C8 | direct (N × H) |
| 238. C3 | C2×D4⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×D4 | 2 |
| D3×C4⋊C8 | 2 |
| C4×D3×C8 | 2 |
| C3×D4⋊C8 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4483 | 2 |
| #4459 | 2 |
| C2×D4⋊C8 | 3 |