Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×#204 | C2 | semidirect |
| 2. C22×D3×C8 | C2 | semidirect |
| 3. C2×#897 | C2 | semidirect |
| 5. C2×C3×#106 | C2 | semidirect |
| 6. C2×#810 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4864 | C2 | direct (N × H) |
| 22. C2×#204 | C22 | semidirect |
| 24. C2×D3×C8 | C22 | semidirect |
| 26. #897 | C22 | semidirect |
| 29. C3×#106 | C22 | semidirect |
| 30. #810 | C22 | semidirect |
| 31. #809 | C22 | semidirect |
| 37. C2×#106 | D3 | semidirect |
| 61. C2×C3×C8 | D4 | semidirect |
| 93. #106 | C2×D3 | semidirect |
| 103. C22×D3 | SD16 | semidirect |
| 127. C3×C8 | C2×D4 | semidirect |
| 154. C2×C8 | D12 | semidirect |
| 174. C2×D3 | C2×SD16 | semidirect |
| 214. C8 | C2×D12 | semidirect |
| 215. C2×C3 | #465 | semidirect |
| 240. C3 | C2×#465 | semidirect |
| 243. C2 | #4864 | 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 |
| C22×D3×C8 | 2 |
| C2×#897 | 2 |
| C2×#895 | 2 |
| C2×C3×#106 | 2 |
| C2×#810 | 2 |
| C2×#809 | 2 |
| #4864 | 2 |
| C2×#465 | 3 |