Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 66 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×Q8×A4 | C2 | semidirect |
| 3. A4×SD16 | C2 | direct (N × H) |
| 4. C2×C8×A4 | C2 | semidirect |
| 5. C23×SD16 | C3 | semidirect |
| 8. Q8×A4 | C22 | semidirect |
| 14. C8×A4 | C22 | semidirect |
| 15. C23×Q8 | C2×C3 | semidirect |
| 22. C22×SD16 | C2×C3 | semidirect |
| 23. C23×C8 | C2×C3 | semidirect |
| 41. C22×Q8 | C22×C3 | semidirect |
| 63. C2×SD16 | A4 | direct (N × H) |
| 67. C22×C8 | C22×C3 | semidirect |
| 70. C2×A4 | SD16 | direct (N × H) |
| 100. C2×Q8 | C2×A4 | semidirect |
| 130. SD16 | C2×A4 | direct (N × H) |
| 136. C2×C8 | C2×A4 | semidirect |
| 140. A4 | C2×SD16 | direct (N × H) |
| 161. C23 | C3×SD16 | semidirect |
| 170. Q8 | C22×A4 | semidirect |
| 195. C8 | C22×A4 | semidirect |
| 216. C22 | C2×C3×SD16 | semidirect |
| 230. C2 | A4×SD16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×A4 | 2 |
| C2×D4×A4 | 2 |
| A4×SD16 | 2 |
| C2×C8×A4 | 2 |
| C23×SD16 | 3 |
| C2×C3×SD16 | 4 |