Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1880 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 981 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 |
|---|---|---|
| 3. C2×C3⋊#95 | C2 | direct (N × H) |
| 7. C23×C3×C4 | C4 | semidirect |
| 11. C23×Dic3 | C4 | semidirect |
| 13. C3⋊#95 | C22 | direct (N × H) |
| 25. C22×C3×C4 | C2×C4 | semidirect |
| 30. C22×Dic3 | C2×C4 | semidirect |
| 38. C23×C4 | Dic3 | semidirect |
| 54. C2×C3×C4 | C22×C4 | semidirect |
| 58. C2×Dic3 | C22×C4 | semidirect |
| 72. C22×C4 | C2×Dic3 | semidirect |
| 74. C22×C3 | #95 | semidirect |
| 104. C2×C4 | C22×Dic3 | semidirect |
| 105. C2×C3 | C2×#95 | semidirect |
| 111. C22 | C3⋊#95 | direct (N × H) |
| 124. C3 | C22×#95 | semidirect |
| 125. C2 | C2×C3⋊#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C24×Dic3 | 2 |
| C2×C3⋊#95 | 2 |
| C22×#95 | 3 |