Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. Dic3×M16 | C2 | semidirect |
| 5. C42×Dic3 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 12. Q8×Dic3 | C4 | semidirect |
| 14. D4×Dic3 | C4 | semidirect |
| 22. C3×#104 | C4 | semidirect |
| 23. #837 | C4 | semidirect |
| 47. C3×M16 | C2×C4 | semidirect |
| 50. C3×C42 | C2×C4 | semidirect |
| 60. C4×Dic3 | C2×C4 | semidirect |
| 64. #208 | C2×C4 | semidirect |
| 80. #104 | Dic3 | direct (N × H) |
| 86. C3×Q8 | C42 | semidirect |
| 90. C3×D4 | C42 | semidirect |
| 127. M16 | C2×Dic3 | semidirect |
| 143. C42 | C2×Dic3 | semidirect |
| 159. Dic3 | #104 | direct (N × H) |
| 163. Q8 | C4×Dic3 | semidirect |
| 167. D4 | C4×Dic3 | semidirect |
| 209. C3 | C4×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×#41 | 2 |
| C2×C3×#104 | 2 |
| C2×#837 | 2 |
| Dic3×M16 | 2 |
| C42×Dic3 | 2 |
| #4555 | 2 |
| #4523 | 2 |
| C4×#104 | 3 |