Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 133 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. Q8×Dic6 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5080 | C2 | semidirect |
| 7. #4855 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4791 | C2 | semidirect |
| 49. #475 | D3 | semidirect |
| 70. #215 | Q8 | semidirect |
| 117. C3×Q8 | C2×Q8 | semidirect |
| 135. Dic6 | SD16 | semidirect |
| 138. C3⋊C8 | C2×Q8 | semidirect |
| 193. Q8 | D3×Q8 | semidirect |
| 230. C3 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| Q8×Dic6 | 2 |
| C3×#475 | 2 |
| #5080 | 2 |
| C4×#215 | 2 |
| #4870 | 2 |
| #4855 | 2 |
| #4842 | 2 |
| #4830 | 2 |
| #4791 | 2 |
| #4788 | 2 |
| Q8×SD16 | 3 |