Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 616 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×D24 | C2 | semidirect |
| 2. C22×D3×C8 | C2 | semidirect |
| 3. C2×#895 | C2 | semidirect |
| 4. C2×C3×#107 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 6. #4883 | C2 | direct (N × H) |
| 16. C2×D24 | C22 | semidirect |
| 18. C2×D3×C8 | C22 | semidirect |
| 20. #895 | C22 | semidirect |
| 21. C3×#107 | C22 | semidirect |
| 22. #809 | C22 | semidirect |
| 27. C2×#107 | D3 | semidirect |
| 44. C2×C3×C8 | D4 | semidirect |
| 66. #107 | C2×D3 | semidirect |
| 75. C22×D3 | D8 | semidirect |
| 92. C3×C8 | C2×D4 | semidirect |
| 113. C2×C8 | D12 | semidirect |
| 129. C2×D3 | C2×D8 | semidirect |
| 160. C8 | C2×D12 | semidirect |
| 161. C2×C3 | #466 | semidirect |
| 184. C3 | C2×#466 | semidirect |
| 187. C2 | #4883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C22×D3×C8 | 2 |
| C2×#895 | 2 |
| C2×C3×#107 | 2 |
| C2×#809 | 2 |
| #4883 | 2 |
| C2×#466 | 3 |