Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#216 | C2 | semidirect |
| 3. C22×Dic12 | C2 | semidirect |
| 5. C2×C3×#103 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4809 | C2 | direct (N × H) |
| 23. C2×#216 | C22 | semidirect |
| 28. C2×Dic12 | C22 | semidirect |
| 31. C3×#103 | C22 | semidirect |
| 33. #810 | C22 | semidirect |
| 40. C2×#103 | D3 | semidirect |
| 104. #103 | C2×D3 | semidirect |
| 109. C22×D3 | Q16 | semidirect |
| 188. C2×D3 | C2×Q16 | semidirect |
| 232. C2×C3 | #451 | semidirect |
| 253. C3 | C2×#451 | semidirect |
| 255. C2 | #4809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C22×#216 | 2 |
| C22×Dic12 | 2 |
| C2×#897 | 2 |
| C2×C3×#103 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#810 | 2 |
| #4809 | 2 |
| C2×#451 | 3 |