Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 2. C22×C3×Q16 | C2 | semidirect |
| 3. C22×#216 | C2 | semidirect |
| 4. C2×D3×Q16 | C2 | direct (N × H) |
| 5. C22×Dic12 | C2 | semidirect |
| 15. C2×C3×Q16 | C22 | semidirect |
| 17. C2×#216 | C22 | semidirect |
| 19. D3×Q16 | C22 | direct (N × H) |
| 20. C2×Dic12 | C22 | semidirect |
| 26. C22×Q16 | D3 | direct (N × H) |
| 43. C3×Q16 | C23 | semidirect |
| 45. #216 | C23 | semidirect |
| 47. Dic12 | C23 | semidirect |
| 59. C2×Q16 | C2×D3 | direct (N × H) |
| 64. C22×D3 | Q16 | direct (N × H) |
| 98. Q16 | C22×D3 | direct (N × H) |
| 102. C22×C3 | C2×Q16 | semidirect |
| 104. C2×D3 | C2×Q16 | direct (N × H) |
| 129. C2×C3 | C22×Q16 | semidirect |
| 131. D3 | C22×Q16 | direct (N × H) |
| 134. C22 | D3×Q16 | direct (N × H) |
| 141. C3 | C23×Q16 | semidirect |
| 143. C2 | C2×D3×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C22×C3×Q16 | 2 |
| C22×#216 | 2 |
| C2×D3×Q16 | 2 |
| C22×Dic12 | 2 |
| C22×D3×C8 | 2 |
| C23×Q16 | 3 |