Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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. #5504 | C2 | semidirect |
| 3. C2×C3×#102 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. #5110 | C2 | semidirect |
| 6. #5106 | C2 | semidirect |
| 7. #4964 | C2 | semidirect |
| 8. #4784 | C2 | semidirect |
| 9. #4779 | C2 | semidirect |
| 10. #4777 | C2 | semidirect |
| 11. #4774 | C2 | semidirect |
| 27. #892 | C22 | semidirect |
| 28. D3×C4⋊C4 | C22 | semidirect |
| 34. (C2×D3)⋊C8 | C22 | semidirect |
| 35. (C2×D3)⋊C8 | C22 | semidirect |
| 36. #818 | C22 | semidirect |
| 37. #818 | C22 | semidirect |
| 38. #817 | C22 | semidirect |
| 39. #817 | C22 | semidirect |
| 40. #808 | C22 | semidirect |
| 41. #807 | C22 | semidirect |
| 51. C2×#102 | D3 | semidirect |
| 262. C3 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5805 | 2 |
| #5504 | 2 |
| C2×C3×#102 | 2 |
| #5215 | 2 |
| #5110 | 2 |
| #5106 | 2 |
| #4964 | 2 |
| #4784 | 2 |
| #4779 | 2 |
| #4777 | 2 |
| #4774 | 2 |
| #3096 | 3 |