Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #4848 | C2 | semidirect |
| 5. #4731 | C2 | semidirect |
| 6. #4694 | C2 | semidirect |
| 7. #4693 | C2 | semidirect |
| 16. C2×#204 | C22 | semidirect |
| 22. #869 | C22 | semidirect |
| 23. #869 | C22 | semidirect |
| 25. C4×Dic6 | C22 | semidirect |
| 26. C3×C4⋊C8 | C22 | semidirect |
| 28. C3×C4×C8 | C22 | semidirect |
| 29. #821 | C22 | semidirect |
| 36. #431 | D3 | semidirect |
| 83. C4⋊C8 | C2×D3 | semidirect |
| 86. C4×C8 | C2×D3 | semidirect |
| 94. C2×C3×C4 | SD16 | semidirect |
| 174. C2×C4 | #204 | semidirect |
| 203. C3 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| #5470 | 2 |
| C3×#431 | 2 |
| #4848 | 2 |
| #4731 | 2 |
| #4694 | 2 |
| #4693 | 2 |
| #3208 | 3 |