Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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×#430 | C2 | semidirect |
| 4. #5125 | C2 | semidirect |
| 5. C2×#822 | C2 | semidirect |
| 6. #4893 | C2 | semidirect |
| 7. D3×#108 | C2 | semidirect |
| 28. #430 | D3 | semidirect |
| 146. C3 | #2916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5745 | 2 |
| C2×#907 | 2 |
| C3×#430 | 2 |
| #5125 | 2 |
| C2×#822 | 2 |
| #4893 | 2 |
| D3×#108 | 2 |
| #2916 | 3 |