Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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. #5827 | C2 | semidirect |
| 3. #5234 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. #5035 | C2 | semidirect |
| 7. #5035 | C2 | semidirect |
| 8. #5034 | C2 | semidirect |
| 9. #5033 | C2 | semidirect |
| 10. #4998 | C2 | semidirect |
| 11. #4995 | C2 | semidirect |
| 25. #926 | C22 | semidirect |
| 27. C2×C4⋊Dic3 | C22 | semidirect |
| 34. #830 | C22 | semidirect |
| 35. #830 | C22 | semidirect |
| 36. #808 | C22 | semidirect |
| 37. #808 | C22 | semidirect |
| 38. #808 | C22 | semidirect |
| 39. #807 | C22 | semidirect |
| 40. #807 | C22 | semidirect |
| 41. #807 | C22 | semidirect |
| 262. C3 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5827 | 2 |
| #5234 | 2 |
| #5215 | 2 |
| C2×#832 | 2 |
| #5035 | 2 |
| #5034 | 2 |
| #5033 | 2 |
| #4998 | 2 |
| #4995 | 2 |
| #3096 | 3 |