Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#926 | C2 | semidirect |
| 3. C3×#407 | C2 | semidirect |
| 4. #5131 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. #4737 | C2 | semidirect |
| 7. #4736 | C2 | semidirect |
| 8. #4735 | C2 | semidirect |
| 23. #926 | C22 | semidirect |
| 25. C2×C4⋊Dic3 | C22 | semidirect |
| 26. C2×C4⋊Dic3 | C22 | semidirect |
| 28. C3×C22⋊C8 | C22 | semidirect |
| 29. C3×C22⋊C8 | C22 | semidirect |
| 30. #821 | C22 | semidirect |
| 31. #821 | C22 | semidirect |
| 32. #818 | C22 | semidirect |
| 33. #817 | C22 | semidirect |
| 41. #407 | D3 | semidirect |
| 96. C22⋊C8 | C2×D3 | semidirect |
| 97. C22⋊C8 | C2×D3 | semidirect |
| 243. C3 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C2×#926 | 2 |
| C3×#407 | 2 |
| #5131 | 2 |
| #5121 | 2 |
| #4737 | 2 |
| #4736 | 2 |
| #4735 | 2 |
| #3094 | 3 |