Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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×#501 | C2 | semidirect |
| 4. #5081 | C2 | semidirect |
| 5. #5064 | C2 | semidirect |
| 7. #4876 | C2 | semidirect |
| 9. #4856 | C2 | semidirect |
| 11. #4702 | C2 | semidirect |
| 51. #501 | D3 | direct (N × H) |
| 91. D3×C8 | Q8 | semidirect |
| 145. C3×C8 | C2×Q8 | semidirect |
| 146. C3⋊C8 | C2×Q8 | semidirect |
| 223. C8 | D3×Q8 | semidirect |
| 227. D3 | #501 | direct (N × H) |
| 244. C3 | C2×#501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C4⋊Q8 | 2 |
| D3×#125 | 2 |
| C3×#501 | 2 |
| #5081 | 2 |
| #5064 | 2 |
| D3×#107 | 2 |
| #4876 | 2 |
| D3×#106 | 2 |
| #4856 | 2 |
| D3×#97 | 2 |
| #4702 | 2 |
| C2×#501 | 3 |