Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
432 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 217 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. D3×C4⋊C8 | C2 | semidirect |
| 6. C8×D12 | C2 | semidirect |
| 7. #4685 | C2 | semidirect |
| 27. C8×Q8 | D3 | semidirect |
| 33. #239 | C8 | semidirect |
| 67. C3×Q8 | C2×C8 | semidirect |
| 74. D12 | C2×C8 | semidirect |
| 78. C4×D3 | C2×C8 | semidirect |
| 113. Q8 | D3×C8 | semidirect |
| 144. C3 | #2988 | 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 |
| D3×C4⋊C8 | 2 |
| C8×D12 | 2 |
| #4685 | 2 |
| #2988 | 3 |