Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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×C3×C4×C8 | C2 | semidirect |
| 3. #4925 | C2 | semidirect |
| 4. #4459 | C2 | semidirect |
| 5. #4456 | C2 | semidirect |
| 26. C2×C4×C8 | D3 | semidirect |
| 34. #235 | C8 | semidirect |
| 91. D12 | C2×C8 | semidirect |
| 96. Dic6 | C2×C8 | semidirect |
| 191. C3 | #1476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C2×C3×C4×C8 | 2 |
| #4925 | 2 |
| #4459 | 2 |
| #4456 | 2 |
| #1476 | 3 |