Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #5504 | C2 | semidirect |
| 3. C3×#390 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. C2×#805 | C2 | semidirect |
| 6. #4530 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 16. #932 | C4 | semidirect |
| 33. #390 | D3 | semidirect |
| 42. C2×C3×D4 | C2×C4 | semidirect |
| 72. #208 | C2×C4 | semidirect |
| 123. D12 | C22⋊C4 | semidirect |
| 128. Dic6 | C22⋊C4 | semidirect |
| 144. C2×D4 | C4×D3 | semidirect |
| 257. C3 | #1883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#932 | 2 |
| #5504 | 2 |
| C3×#390 | 2 |
| #5215 | 2 |
| C2×#805 | 2 |
| #4530 | 2 |
| #4523 | 2 |
| #1883 | 3 |