Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 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. #5830 | C2 | semidirect |
| 3. C2×#949 | C2 | semidirect |
| 4. C22×#215 | C2 | semidirect |
| 5. #5238 | C2 | semidirect |
| 6. #5234 | C2 | semidirect |
| 7. #5233 | C2 | semidirect |
| 8. #5227 | C2 | semidirect |
| 9. #5225 | C2 | semidirect |
| 17. C2×C3×#41 | C22 | semidirect |
| 20. C22×C3×Q8 | C22 | semidirect |
| 34. #835 | C22 | semidirect |
| 35. #835 | C22 | semidirect |
| 36. #832 | C22 | semidirect |
| 37. #830 | C22 | semidirect |
| 38. C2×2−1+4 | D3 | semidirect |
| 55. C3×#41 | D4 | semidirect |
| 63. C2×C3×Q8 | D4 | semidirect |
| 99. C2×#41 | C2×D3 | semidirect |
| 102. C22×Q8 | C2×D3 | semidirect |
| 167. #41 | #67 | semidirect |
| 175. C2×Q8 | #67 | semidirect |
| 284. C3 | #3010 | semidirect |
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 |
| #5830 | 2 |
| C2×#949 | 2 |
| C22×#215 | 2 |
| #5238 | 2 |
| #5234 | 2 |
| #5233 | 2 |
| #5227 | 2 |
| #5225 | 2 |
| #3010 | 3 |