Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 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. #5211 | C2 | direct (N × H) |
| 4. C2×C3⋊#95 | C2 | semidirect |
| 8. C23×C3×C4 | C4 | semidirect |
| 14. C3⋊#95 | C22 | semidirect |
| 28. C22×C3×C4 | C2×C4 | semidirect |
| 37. C23×C4 | Dic3 | semidirect |
| 72. C22×C4 | C2×Dic3 | semidirect |
| 105. C2×C3 | #381 | semidirect |
| 121. C3 | C2×#381 | semidirect |
| 123. C2 | #5211 | 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 |
| C22×#217 | 2 |
| #5211 | 2 |
| C2×C3⋊#95 | 2 |
| C2×#381 | 3 |