Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C2×C4×Dic6 | C2 | semidirect |
| 4. C2×C3×C4×C8 | C2 | semidirect |
| 6. C2×#817 | C2 | semidirect |
| 7. C2×#816 | C2 | semidirect |
| 8. C4×#204 | C2 | direct (N × H) |
| 21. C2×#204 | C4 | direct (N × H) |
| 26. C4×Dic6 | C22 | semidirect |
| 27. C3×C4×C8 | C22 | semidirect |
| 29. #817 | C22 | semidirect |
| 30. #816 | C22 | semidirect |
| 38. C2×C4×C8 | D3 | semidirect |
| 54. C2×Dic6 | C2×C4 | semidirect |
| 57. C2×C3×C8 | C2×C4 | semidirect |
| 69. #204 | C2×C4 | direct (N × H) |
| 90. C4×C8 | C2×D3 | semidirect |
| 97. C2×C3×C4 | SD16 | semidirect |
| 116. Dic6 | C22×C4 | semidirect |
| 118. C3×C8 | C22×C4 | semidirect |
| 138. C2×C8 | C4×D3 | semidirect |
| 160. C3×C4 | C2×SD16 | semidirect |
| 185. C2×C4 | #204 | direct (N × H) |
| 193. C8 | C2×C4×D3 | semidirect |
| 194. C2×C3 | C4×SD16 | semidirect |
| 212. C4 | C2×#204 | direct (N × H) |
| 215. C3 | C2×C4×SD16 | semidirect |
| 217. C2 | C4×#204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×C4×D12 | 2 |
| C2×C4×Dic6 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#821 | 2 |
| C2×#817 | 2 |
| C2×#816 | 2 |
| C4×#204 | 2 |
| C2×C4×SD16 | 3 |