Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. C3×#324 | C2 | semidirect |
| 4. #4528 | C2 | semidirect |
| 5. #4469 | C2 | semidirect |
| 24. #324 | D3 | direct (N × H) |
| 39. C2×C4×D3 | C8 | semidirect |
| 74. C2×C3×C4 | C2×C8 | semidirect |
| 82. C2×Dic3 | C2×C8 | semidirect |
| 159. C2×C4 | D3×C8 | semidirect |
| 169. D3 | #324 | direct (N × H) |
| 189. C3 | C2×#324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C4⋊C4 | 2 |
| D3×C22⋊C8 | 2 |
| C3×#324 | 2 |
| #4528 | 2 |
| #4469 | 2 |
| C2×#324 | 3 |