Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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×#1010 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. C2×#875 | C2 | semidirect |
| 5. C2×C3×#104 | C2 | semidirect |
| 6. C2×#824 | C2 | semidirect |
| 7. C2×#805 | C2 | semidirect |
| 8. #4827 | C2 | direct (N × H) |
| 14. #1010 | C22 | semidirect |
| 26. #949 | C22 | semidirect |
| 32. #908 | C22 | semidirect |
| 36. #875 | C22 | semidirect |
| 37. C3×#104 | C22 | semidirect |
| 38. #824 | C22 | semidirect |
| 39. #805 | C22 | semidirect |
| 46. C2×#104 | D3 | semidirect |
| 135. #104 | C2×D3 | semidirect |
| 319. C2×C3 | #454 | semidirect |
| 343. C3 | C2×#454 | semidirect |
| 349. C2 | #4827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C2×#949 | 2 |
| C2×#908 | 2 |
| C2×#875 | 2 |
| C2×C3×#104 | 2 |
| C2×#824 | 2 |
| C2×#805 | 2 |
| #4827 | 2 |
| C2×#454 | 3 |