Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#869 | C2 | semidirect |
| 3. C3×#423 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. #4851 | C2 | semidirect |
| 7. #4850 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4842 | C2 | semidirect |
| 43. #423 | D3 | semidirect |
| 51. #235 | Q8 | semidirect |
| 124. D12 | C2×Q8 | semidirect |
| 131. Dic6 | C2×Q8 | semidirect |
| 237. C3 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C2×#869 | 2 |
| C3×#423 | 2 |
| #5133 | 2 |
| #5121 | 2 |
| #4851 | 2 |
| #4850 | 2 |
| #4846 | 2 |
| #4842 | 2 |
| #3079 | 3 |