Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5519 | C2 | semidirect |
| 3. C3×#405 | C2 | semidirect |
| 4. #5133 | C2 | semidirect |
| 5. #5131 | C2 | semidirect |
| 6. #5113 | C2 | semidirect |
| 7. C2×#821 | C2 | semidirect |
| 8. #4714 | C2 | semidirect |
| 9. #4713 | C2 | semidirect |
| 10. #4697 | C2 | semidirect |
| 11. #4694 | C2 | semidirect |
| 28. #870 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. C3×#97 | C22 | semidirect |
| 31. C3×C4×C8 | C22 | semidirect |
| 36. #821 | C22 | semidirect |
| 37. #821 | C22 | semidirect |
| 38. #821 | C22 | semidirect |
| 39. #816 | C22 | semidirect |
| 40. #816 | C22 | semidirect |
| 41. #816 | C22 | semidirect |
| 52. #405 | D3 | semidirect |
| 116. #97 | C2×D3 | semidirect |
| 117. C4×C8 | C2×D3 | semidirect |
| 264. C3 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5525 | 2 |
| #5519 | 2 |
| C3×#405 | 2 |
| #5133 | 2 |
| #5131 | 2 |
| #5113 | 2 |
| C2×#821 | 2 |
| #4714 | 2 |
| #4713 | 2 |
| #4697 | 2 |
| #4694 | 2 |
| #3136 | 3 |