Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
| 3. C2×#869 | C2 | semidirect |
| 4. C2×C3×C4×C8 | C2 | semidirect |
| 5. #4693 | C2 | direct (N × H) |
| 14. C2×#204 | C22 | semidirect |
| 18. #869 | C22 | semidirect |
| 19. C3×C4×C8 | C22 | semidirect |
| 24. C2×C4×C8 | D3 | semidirect |
| 37. C2×C3×C8 | D4 | semidirect |
| 55. C4×C8 | C2×D3 | semidirect |
| 60. C2×C3×C4 | SD16 | semidirect |
| 72. C3×C8 | C2×D4 | semidirect |
| 86. C2×C8 | D12 | semidirect |
| 98. C3×C4 | C2×SD16 | semidirect |
| 112. C2×C4 | #204 | semidirect |
| 117. C8 | C2×D12 | semidirect |
| 118. C2×C3 | #492 | semidirect |
| 130. C4 | C2×#204 | semidirect |
| 132. C3 | C2×#492 | semidirect |
| 134. C2 | #4693 | 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×#874 | 2 |
| C2×#869 | 2 |
| C2×C3×C4×C8 | 2 |
| #4693 | 2 |
| C2×#492 | 3 |