Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#239 | C2 | semidirect |
| 2. C2×C3×#137 | C2 | semidirect |
| 3. #5828 | C2 | semidirect |
| 4. C2×#949 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5187 | C2 | semidirect |
| 7. #5172 | C2 | semidirect |
| 8. #5131 | C2 | semidirect |
| 9. #5126 | C2 | semidirect |
| 22. C2×C3×Q16 | C22 | semidirect |
| 23. C2×C3×SD16 | C22 | semidirect |
| 26. #946 | C22 | semidirect |
| 27. C2×#215 | C22 | semidirect |
| 28. #938 | C22 | semidirect |
| 31. C2×#213 | C22 | semidirect |
| 35. #835 | C22 | semidirect |
| 36. #821 | C22 | semidirect |
| 37. (C2×D3)⋊C8 | C22 | semidirect |
| 39. C2×#137 | D3 | semidirect |
| 53. C2×C3×Q8 | D4 | semidirect |
| 70. C2×D12 | D4 | semidirect |
| 104. C2×Q16 | C2×D3 | semidirect |
| 106. C2×SD16 | C2×D3 | semidirect |
| 166. C2×Q8 | #67 | semidirect |
| 284. C3 | #3005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C2×C3×#137 | 2 |
| #5828 | 2 |
| C2×#949 | 2 |
| #5225 | 2 |
| #5187 | 2 |
| #5172 | 2 |
| #5131 | 2 |
| #5126 | 2 |
| #3005 | 3 |