Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 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×#204 | C2 | semidirect |
| 3. C2×#875 | C2 | semidirect |
| 4. C2×#874 | C2 | semidirect |
| 5. C2×C3×#97 | C2 | semidirect |
| 6. #4712 | C2 | direct (N × H) |
| 16. C2×D24 | C22 | semidirect |
| 18. C2×#204 | C22 | semidirect |
| 20. #875 | C22 | semidirect |
| 22. #874 | C22 | semidirect |
| 23. C3×#97 | C22 | semidirect |
| 29. C2×#97 | D3 | semidirect |
| 47. C2×C3×C8 | D4 | semidirect |
| 69. #97 | C2×D3 | semidirect |
| 92. C3×C8 | C2×D4 | semidirect |
| 112. C2×C8 | D12 | semidirect |
| 152. C8 | C2×D12 | semidirect |
| 153. C2×C3 | #496 | semidirect |
| 171. C3 | C2×#496 | semidirect |
| 174. C2 | #4712 | 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×#204 | 2 |
| C2×#875 | 2 |
| C2×#874 | 2 |
| C2×C3×#97 | 2 |
| #4712 | 2 |
| C2×#496 | 3 |