Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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. #5470 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4842 | C2 | semidirect |
| 5. #4841 | C2 | semidirect |
| 7. #4721 | C2 | semidirect |
| 8. C4×#204 | C2 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 27. C4×Dic6 | C22 | semidirect |
| 28. C3×C4⋊C8 | C22 | semidirect |
| 30. C3×C4×C8 | C22 | semidirect |
| 32. #817 | C22 | semidirect |
| 33. #816 | C22 | semidirect |
| 41. #431 | D3 | semidirect |
| 92. C4⋊C8 | C2×D3 | semidirect |
| 96. C4×C8 | C2×D3 | semidirect |
| 104. C2×C3×C4 | SD16 | semidirect |
| 189. C2×C4 | #204 | semidirect |
| 219. C3 | #3101 | 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×#431 | 2 |
| #4842 | 2 |
| #4841 | 2 |
| #4731 | 2 |
| #4721 | 2 |
| C4×#204 | 2 |
| #3101 | 3 |