Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 500 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×#431 | C2 | semidirect |
| 3. #4925 | C2 | semidirect |
| 4. #4834 | C2 | semidirect |
| 5. D3×C22⋊C8 | C2 | semidirect |
| 6. C8×D12 | C2 | semidirect |
| 13. C2×D3×C8 | C22 | semidirect |
| 18. C3×C4⋊C8 | C22 | semidirect |
| 20. C3×C4×C8 | C22 | semidirect |
| 22. (C2×D3)⋊C8 | C22 | semidirect |
| 23. C4⋊(C3⋊C8) | C22 | semidirect |
| 24. C4×C3⋊C8 | C22 | semidirect |
| 29. #431 | D3 | semidirect |
| 36. C2×D12 | C8 | semidirect |
| 64. C4⋊C8 | C2×D3 | semidirect |
| 69. C4×C8 | C2×D3 | semidirect |
| 73. C22×D3 | C2×C8 | semidirect |
| 77. C2×C3×C4 | C2×C8 | semidirect |
| 86. D12 | C2×C8 | semidirect |
| 87. D12 | C2×C8 | semidirect |
| 142. C2×C4 | D3×C8 | semidirect |
| 171. C3 | #2972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×#431 | 2 |
| #4925 | 2 |
| #4834 | 2 |
| D3×C22⋊C8 | 2 |
| C8×D12 | 2 |
| #2972 | 3 |