Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×C3×#131 | C2 | semidirect |
| 2. C2×#951 | C2 | semidirect |
| 4. C22×#204 | C2 | semidirect |
| 5. #5141 | C2 | direct (N × H) |
| 6. C2×#824 | C2 | semidirect |
| 7. C2×#823 | C2 | semidirect |
| 8. C2×#819 | C2 | semidirect |
| 14. C3×#131 | C22 | semidirect |
| 20. #951 | C22 | semidirect |
| 32. C2×#204 | C22 | semidirect |
| 33. #824 | C22 | semidirect |
| 34. #823 | C22 | semidirect |
| 35. #819 | C22 | semidirect |
| 39. C2×#131 | D3 | semidirect |
| 104. #131 | C2×D3 | semidirect |
| 251. C2×C3 | #471 | semidirect |
| 270. C3 | C2×#471 | semidirect |
| 275. C2 | #5141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C2×#951 | 2 |
| C2×#949 | 2 |
| C22×#204 | 2 |
| #5141 | 2 |
| C2×#824 | 2 |
| C2×#823 | 2 |
| C2×#819 | 2 |
| C2×#471 | 3 |