Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5517 | C2 | semidirect |
| 3. C3×#418 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. #5131 | C2 | semidirect |
| 6. Dic3×M16 | C2 | semidirect |
| 7. #5001 | C2 | semidirect |
| 8. #4764 | C2 | semidirect |
| 9. #4760 | C2 | semidirect |
| 22. #890 | C22 | semidirect |
| 23. #888 | C22 | semidirect |
| 26. C3×#102 | C22 | semidirect |
| 27. #832 | C22 | semidirect |
| 28. #821 | C22 | semidirect |
| 29. #815 | C22 | semidirect |
| 30. C8×Dic3 | C22 | semidirect |
| 31. #809 | C22 | semidirect |
| 39. #418 | D3 | semidirect |
| 91. #102 | C2×D3 | semidirect |
| 217. C3 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| #5517 | 2 |
| C3×#418 | 2 |
| #5215 | 2 |
| #5131 | 2 |
| Dic3×M16 | 2 |
| #5001 | 2 |
| #4764 | 2 |
| #4760 | 2 |
| #3138 | 3 |