Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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. #5833 | C2 | semidirect |
| 3. #5830 | C2 | semidirect |
| 4. C2×#908 | C2 | semidirect |
| 5. #5135 | C2 | semidirect |
| 6. #5134 | C2 | semidirect |
| 7. #5121 | C2 | semidirect |
| 8. #5115 | C2 | semidirect |
| 9. #5114 | C2 | semidirect |
| 10. #5113 | C2 | semidirect |
| 11. C2×#821 | C2 | semidirect |
| 18. C2×C3×M16 | C22 | semidirect |
| 20. C22×C3×C8 | C22 | semidirect |
| 29. #930 | C22 | semidirect |
| 32. #924 | C22 | semidirect |
| 38. #821 | C22 | semidirect |
| 39. #821 | C22 | semidirect |
| 40. #818 | C22 | semidirect |
| 41. #817 | C22 | semidirect |
| 42. #816 | C22 | semidirect |
| 43. #816 | C22 | semidirect |
| 45. C2×#131 | D3 | semidirect |
| 78. C3×M16 | D4 | semidirect |
| 105. C2×M16 | C2×D3 | semidirect |
| 107. C22×C8 | C2×D3 | semidirect |
| 190. M16 | #67 | semidirect |
| 295. C3 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| #5833 | 2 |
| #5830 | 2 |
| C2×#908 | 2 |
| #5135 | 2 |
| #5134 | 2 |
| #5121 | 2 |
| #5115 | 2 |
| #5114 | 2 |
| #5113 | 2 |
| C2×#821 | 2 |
| #3062 | 3 |