Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 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. C3×C8×Q8 | C2 | semidirect |
| 3. Q8×C3⋊C8 | C2 | semidirect |
| 4. #4834 | C2 | semidirect |
| 5. #4833 | C2 | semidirect |
| 6. C8×D12 | C2 | semidirect |
| 7. C4×D3×C8 | C2 | semidirect |
| 27. C8×Q8 | D3 | semidirect |
| 33. #239 | C8 | direct (N × H) |
| 68. C3×Q8 | C2×C8 | semidirect |
| 75. D12 | C2×C8 | semidirect |
| 79. C4×D3 | C2×C8 | semidirect |
| 81. C3×C8 | #41 | semidirect |
| 83. C3⋊C8 | #41 | semidirect |
| 115. Q8 | D3×C8 | semidirect |
| 130. C8 | #239 | direct (N × H) |
| 146. C3 | C8×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#239 | 2 |
| C3×C8×Q8 | 2 |
| Q8×C3⋊C8 | 2 |
| #4834 | 2 |
| #4833 | 2 |
| C8×D12 | 2 |
| C4×D3×C8 | 2 |
| C8×#41 | 3 |