Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 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. C23×C3×Q8 | C2 | semidirect |
| 3. C2×#947 | C2 | direct (N × H) |
| 4. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C22×C4×Dic3 | C2 | semidirect |
| 9. C22×C3×Q8 | C22 | semidirect |
| 15. #947 | C22 | direct (N × H) |
| 16. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic3 | C22 | semidirect |
| 18. C23×Q8 | D3 | semidirect |
| 28. C2×C3×Q8 | C23 | semidirect |
| 37. (C2×D3)⋊C4 | C23 | semidirect |
| 38. C4×Dic3 | C23 | semidirect |
| 41. C22×Q8 | C2×D3 | semidirect |
| 70. C2×Q8 | C22×D3 | semidirect |
| 81. C22×C3 | #124 | semidirect |
| 106. C2×C3 | C2×#124 | semidirect |
| 113. C22 | #947 | direct (N × H) |
| 120. C3 | C22×#124 | semidirect |
| 122. C2 | C2×#947 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Q8 | 2 |
| C23×D12 | 2 |
| C2×#947 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C22×#124 | 3 |