Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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×#432 | C2 | semidirect |
| 4. #4846 | C2 | semidirect |
| 5. #4841 | C2 | semidirect |
| 7. #4722 | C2 | semidirect |
| 8. #4710 | C2 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 27. C4×Dic6 | C22 | semidirect |
| 28. C3×C4⋊C8 | C22 | semidirect |
| 30. C3×#97 | C22 | semidirect |
| 32. #818 | C22 | semidirect |
| 33. #816 | C22 | semidirect |
| 41. #432 | D3 | semidirect |
| 92. C4⋊C8 | C2×D3 | semidirect |
| 96. #97 | C2×D3 | semidirect |
| 219. C3 | #3110 | 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×#432 | 2 |
| #4846 | 2 |
| #4841 | 2 |
| #4731 | 2 |
| #4722 | 2 |
| #4710 | 2 |
| #3110 | 3 |