Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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×C3×2−1+4 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C2×#947 | C2 | semidirect |
| 4. #5245 | C2 | direct (N × H) |
| 5. C2×#837 | C2 | semidirect |
| 6. C2×#836 | C2 | semidirect |
| 10. C3×2−1+4 | C22 | semidirect |
| 18. #949 | C22 | semidirect |
| 20. #947 | C22 | semidirect |
| 26. #837 | C22 | semidirect |
| 27. #836 | C22 | semidirect |
| 28. C2×2−1+4 | D3 | semidirect |
| 73. 2−1+4 | C2×D3 | semidirect |
| 210. C2×C3 | #454 | semidirect |
| 228. C3 | C2×#454 | semidirect |
| 233. C2 | #5245 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×2−1+4 | 2 |
| C2×#949 | 2 |
| C2×#947 | 2 |
| #5245 | 2 |
| C2×#837 | 2 |
| C2×#836 | 2 |
| C2×#454 | 3 |