Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C8 | C22 |
| commutator | C2 | C22×C3×C16 |
| Frattini, cosocle | C2×C8 | C23×C3 |
| socle | C22×C3 | C22×C8 |
| prime radical | C23×C3 | C2×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4⋊C16 | C2 | semidirect |
| 4. C3×C4×C16 | C2 | semidirect |
| 5. #2162 | C3 | direct (N × H) |
| 15. C4⋊C16 | C2×C3 | semidirect |
| 17. C4×C16 | C2×C3 | semidirect |
| 44. C2×C3×C4 | C16 | semidirect |
| 84. C2×C4 | C3×C16 | semidirect |
| 110. C3 | #2162 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C8 | 2 |
| C3×C4⋊C16 | 2 |
| C3×C22⋊C16 | 2 |
| C3×C4×C16 | 2 |
| #2162 | 3 |