Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C3×#380 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. C2×#809 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 6. C2×#808 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 31. #380 | D3 | semidirect |
| 68. C2×C3⋊C8 | D4 | semidirect |
| 277. C3 | #2034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C3×#380 | 2 |
| C2×#830 | 2 |
| C2×#809 | 2 |
| C2×#808 | 2 |
| #4529 | 2 |
| #2034 | 3 |