Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3×#104 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #5118 | C2 | semidirect |
| 6. C42×Dic3 | C2 | semidirect |
| 7. C2×#805 | C2 | semidirect |
| 13. #947 | C4 | semidirect |
| 14. #944 | C4 | semidirect |
| 15. #940 | C4 | semidirect |
| 17. #936 | C4 | semidirect |
| 33. C2×#104 | D3 | semidirect |
| 60. C3×C42 | D4 | semidirect |
| 69. C4×Dic3 | D4 | semidirect |
| 166. C42 | #67 | semidirect |
| 184. Dic3 | #104 | semidirect |
| 246. C3 | #1962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5832 | 2 |
| C2×C3×#104 | 2 |
| C2×#837 | 2 |
| C2×#825 | 2 |
| #5118 | 2 |
| C42×Dic3 | 2 |
| C2×#805 | 2 |
| #1962 | 3 |