Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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×#424 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 7. #5106 | C2 | semidirect |
| 8. #4847 | C2 | semidirect |
| 9. #4847 | C2 | semidirect |
| 10. #4846 | C2 | semidirect |
| 11. #4842 | C2 | semidirect |
| 28. #870 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. C3×C4⋊C8 | C22 | semidirect |
| 31. C3×C4⋊C8 | C22 | semidirect |
| 36. #818 | C22 | semidirect |
| 37. #818 | C22 | semidirect |
| 38. #818 | C22 | semidirect |
| 39. #817 | C22 | semidirect |
| 40. #817 | C22 | semidirect |
| 41. #817 | C22 | semidirect |
| 50. #424 | D3 | semidirect |
| 58. C2×D12 | Q8 | semidirect |
| 110. C4⋊C8 | C2×D3 | semidirect |
| 111. C4⋊C8 | C2×D3 | semidirect |
| 243. C3 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5521 | 2 |
| #5519 | 2 |
| C3×#424 | 2 |
| #5131 | 2 |
| #5121 | 2 |
| C2×#821 | 2 |
| #5106 | 2 |
| #4847 | 2 |
| #4846 | 2 |
| #4842 | 2 |
| #3081 | 3 |