Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5500 | C2 | semidirect |
| 3. C2×C3×#102 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. #5113 | C2 | semidirect |
| 6. #5101 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 8. #4768 | C2 | semidirect |
| 9. #4765 | C2 | semidirect |
| 10. #4764 | C2 | semidirect |
| 11. #4760 | C2 | semidirect |
| 27. #890 | C22 | semidirect |
| 29. #888 | C22 | semidirect |
| 34. #821 | C22 | semidirect |
| 35. #821 | C22 | semidirect |
| 36. #816 | C22 | semidirect |
| 37. #816 | C22 | semidirect |
| 38. #815 | C22 | semidirect |
| 39. C8×Dic3 | C22 | semidirect |
| 40. #810 | C22 | semidirect |
| 41. #809 | C22 | semidirect |
| 51. C2×#102 | 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 |
|---|---|
| #5805 | 2 |
| #5500 | 2 |
| C2×C3×#102 | 2 |
| #5215 | 2 |
| #5113 | 2 |
| #5101 | 2 |
| #4966 | 2 |
| #4768 | 2 |
| #4765 | 2 |
| #4764 | 2 |
| #4760 | 2 |
| #3136 | 3 |