Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×C3×C4⋊Q8 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 4. #5085 | C2 | direct (N × H) |
| 5. C2×C4×C3⋊C8 | C2 | semidirect |
| 11. C3×C4⋊Q8 | C22 | semidirect |
| 15. C2×#215 | C22 | semidirect |
| 19. C4×C3⋊C8 | C22 | semidirect |
| 21. C2×C4⋊Q8 | D3 | semidirect |
| 41. C2×C3⋊C8 | D4 | semidirect |
| 50. C4⋊Q8 | C2×D3 | semidirect |
| 64. C2×C3×C4 | SD16 | semidirect |
| 72. C3⋊C8 | C2×D4 | semidirect |
| 99. C3×C4 | C2×SD16 | semidirect |
| 112. C2×C4 | #215 | semidirect |
| 118. C2×C3 | #492 | semidirect |
| 130. C4 | C2×#215 | semidirect |
| 132. C3 | C2×#492 | semidirect |
| 134. C2 | #5085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| C22×#215 | 2 |
| C2×#874 | 2 |
| #5085 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×#492 | 3 |