Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×D3×Q16 | C2 | semidirect |
| 3. C3×C4×Q16 | C2 | semidirect |
| 4. #5031 | C2 | semidirect |
| 5. #4887 | C2 | semidirect |
| 6. #4809 | C2 | semidirect |
| 7. #4699 | C2 | semidirect |
| 36. C4×Q16 | D3 | semidirect |
| 46. C3×Q16 | D4 | semidirect |
| 94. D12 | Q16 | direct (N × H) |
| 115. Q16 | D12 | direct (N × H) |
| 133. C2×D3 | C2×Q16 | semidirect |
| 137. C3×C4 | C2×Q16 | semidirect |
| 175. C4 | D3×Q16 | semidirect |
| 178. C3 | D4×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| Q8×D12 | 2 |
| C3×C4×Q16 | 2 |
| #5031 | 2 |
| #4887 | 2 |
| #4809 | 2 |
| #4699 | 2 |
| C8×D12 | 2 |
| D4×Q16 | 3 |