Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
| 4. C2×#835 | C2 | semidirect |
| 5. #5083 | C2 | direct (N × H) |
| 6. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 23. #835 | C22 | semidirect |
| 24. C4⋊(C3⋊C8) | C22 | semidirect |
| 26. C2×C4⋊Q8 | D3 | semidirect |
| 64. C4⋊Q8 | C2×D3 | semidirect |
| 85. C2×C3×C4 | SD16 | semidirect |
| 136. C3×C4 | C2×SD16 | semidirect |
| 157. C2×C4 | #215 | semidirect |
| 165. C2×C3 | #461 | semidirect |
| 182. C4 | C2×#215 | semidirect |
| 185. C3 | C2×#461 | semidirect |
| 187. C2 | #5083 | 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×C4×D12 | 2 |
| C2×#835 | 2 |
| #5083 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#461 | 3 |