Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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×C8×Q8 | C2 | semidirect |
| 4. #4848 | C2 | semidirect |
| 5. #4842 | C2 | semidirect |
| 6. #4694 | C2 | semidirect |
| 7. C4×#204 | C2 | semidirect |
| 30. C8×Q8 | D3 | semidirect |
| 68. C3×Q8 | SD16 | semidirect |
| 82. Dic6 | #41 | semidirect |
| 119. Q8 | #204 | semidirect |
| 148. C3 | #3362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5577 | 2 |
| Q8×Dic6 | 2 |
| C3×C8×Q8 | 2 |
| #4848 | 2 |
| #4842 | 2 |
| #4694 | 2 |
| C4×#204 | 2 |
| #3362 | 3 |