Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 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. C3×#518 | C2 | semidirect |
| 2. C22×#214 | C2 | semidirect |
| 4. #5526 | C2 | semidirect |
| 5. #5019 | C2 | semidirect |
| 6. #5016 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 8. #5002 | C2 | semidirect |
| 9. #4999 | C2 | semidirect |
| 28. #875 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. #810 | C22 | semidirect |
| 31. #810 | C22 | semidirect |
| 32. #809 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 37. #518 | D3 | semidirect |
| 227. C3 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#518 | 2 |
| C22×#214 | 2 |
| C2×#932 | 2 |
| #5526 | 2 |
| #5019 | 2 |
| #5016 | 2 |
| #5004 | 2 |
| #5002 | 2 |
| #4999 | 2 |
| #3042 | 3 |