Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#214 | C2 | semidirect |
| 3. C2×#924 | C2 | semidirect |
| 4. C22×#208 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. #5042 | C2 | direct (N × H) |
| 7. C2×#810 | C2 | semidirect |
| 8. C2×#807 | C2 | semidirect |
| 20. C2×#214 | C22 | semidirect |
| 23. #924 | C22 | semidirect |
| 26. C2×#208 | C22 | semidirect |
| 29. #832 | C22 | semidirect |
| 30. #810 | C22 | semidirect |
| 31. #807 | C22 | semidirect |
| 71. C2×C3⋊C8 | D4 | semidirect |
| 128. C3⋊C8 | C2×D4 | semidirect |
| 217. C2×C3 | #468 | semidirect |
| 240. C3 | C2×#468 | semidirect |
| 243. C2 | #5042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#121 | 2 |
| C22×#214 | 2 |
| C2×#924 | 2 |
| C22×#208 | 2 |
| C2×#832 | 2 |
| #5042 | 2 |
| C2×#810 | 2 |
| C2×#807 | 2 |
| C2×#468 | 3 |