Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 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×#239 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 3. C22×D24 | C2 | semidirect |
| 4. C2×#895 | C2 | semidirect |
| 5. C2×C3×#103 | C2 | semidirect |
| 6. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4810 | C2 | direct (N × H) |
| 14. C2×#239 | C22 | semidirect |
| 24. C2×#215 | C22 | semidirect |
| 28. C2×D24 | C22 | semidirect |
| 30. #895 | C22 | semidirect |
| 31. C3×#103 | C22 | semidirect |
| 32. (C2×D3)⋊C8 | C22 | semidirect |
| 33. #809 | C22 | semidirect |
| 39. C2×#103 | D3 | semidirect |
| 47. C2×C3×Q8 | D4 | semidirect |
| 65. C2×D12 | D4 | semidirect |
| 104. #103 | C2×D3 | semidirect |
| 122. C3×Q8 | C2×D4 | semidirect |
| 140. D12 | C2×D4 | semidirect |
| 155. C2×Q8 | D12 | semidirect |
| 225. Q8 | C2×D12 | semidirect |
| 250. C2×C3 | #449 | semidirect |
| 279. C3 | C2×#449 | semidirect |
| 283. C2 | #4810 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C22×#215 | 2 |
| C22×D24 | 2 |
| C2×#895 | 2 |
| C2×C3×#103 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#809 | 2 |
| #4810 | 2 |
| C2×#449 | 3 |