Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #5470 | C2 | semidirect |
| 3. C3×#423 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. #4847 | C2 | semidirect |
| 7. #4846 | C2 | semidirect |
| 8. #4842 | C2 | semidirect |
| 23. #870 | C22 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 28. C3×C4⋊C8 | C22 | semidirect |
| 29. C3×C4⋊C8 | C22 | semidirect |
| 32. #818 | C22 | semidirect |
| 33. #817 | C22 | semidirect |
| 40. #423 | D3 | semidirect |
| 49. C2×D12 | Q8 | semidirect |
| 94. C4⋊C8 | C2×D3 | semidirect |
| 95. C4⋊C8 | C2×D3 | semidirect |
| 225. C3 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| #5470 | 2 |
| C3×#423 | 2 |
| #5131 | 2 |
| #5121 | 2 |
| #4847 | 2 |
| #4846 | 2 |
| #4842 | 2 |
| #3077 | 3 |