Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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. #5019 | C2 | semidirect |
| 3. #4846 | C2 | semidirect |
| 4. #4694 | C2 | semidirect |
| 5. C3×D4⋊C8 | C2 | semidirect |
| 6. #4485 | C2 | semidirect |
| 7. #4459 | C2 | semidirect |
| 18. #869 | C22 | semidirect |
| 19. C3×C4⋊C8 | C22 | semidirect |
| 20. C3×C4×C8 | C22 | semidirect |
| 25. C4⋊(C3⋊C8) | C22 | semidirect |
| 32. D4⋊C8 | D3 | semidirect |
| 72. C4⋊C8 | C2×D3 | semidirect |
| 76. C4×C8 | C2×D3 | semidirect |
| 101. D12 | SD16 | semidirect |
| 212. C3 | #1639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D12 | 2 |
| #5019 | 2 |
| #4846 | 2 |
| #4694 | 2 |
| C3×D4⋊C8 | 2 |
| #4485 | 2 |
| #4459 | 2 |
| #1639 | 3 |