Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#869 | C2 | semidirect |
| 3. C2×C3×C4⋊C8 | C2 | semidirect |
| 5. C2×#817 | C2 | semidirect |
| 6. #4842 | C2 | direct (N × H) |
| 20. #869 | C22 | semidirect |
| 21. C3×C4⋊C8 | C22 | semidirect |
| 23. #817 | C22 | semidirect |
| 28. C2×C4⋊C8 | D3 | semidirect |
| 38. C2×D12 | Q8 | semidirect |
| 68. C4⋊C8 | C2×D3 | semidirect |
| 89. D12 | C2×Q8 | semidirect |
| 155. C2×C3 | #476 | semidirect |
| 175. C3 | C2×#476 | semidirect |
| 177. C2 | #4842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C2×#869 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#821 | 2 |
| C2×#817 | 2 |
| #4842 | 2 |
| C2×#476 | 3 |