Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
794 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C3×#123 | C2 | semidirect |
| 3. C2×#929 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 5. #5053 | C2 | direct (N × H) |
| 6. C2×#806 | C2 | semidirect |
| 9. C23×C3×C4 | C22 | semidirect |
| 19. C3×#123 | C22 | semidirect |
| 22. C2×C3×C22⋊C4 | C22 | semidirect |
| 23. C2×#217 | C22 | semidirect |
| 25. #929 | C22 | semidirect |
| 28. #834 | C22 | semidirect |
| 29. #806 | C22 | semidirect |
| 32. C2×#123 | D3 | semidirect |
| 50. C22×C3×C4 | C23 | semidirect |
| 75. C3×C22⋊C4 | C23 | semidirect |
| 77. #217 | C23 | semidirect |
| 89. C23×C4 | C2×D3 | semidirect |
| 93. #123 | C2×D3 | semidirect |
| 99. C2×C22⋊C4 | C2×D3 | semidirect |
| 179. C22×C4 | C22×D3 | semidirect |
| 187. C22⋊C4 | C22×D3 | semidirect |
| 259. C2×C3 | #458 | semidirect |
| 286. C3 | C2×#458 | semidirect |
| 293. C2 | #5053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| C2×C3×#123 | 2 |
| C2×#929 | 2 |
| C2×#834 | 2 |
| #5053 | 2 |
| C2×#806 | 2 |
| C2×#458 | 3 |