Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
300 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×C22⋊C4 |
| commutator | C23 | C22×C3×C4 |
| Frattini, cosocle | C24 | C23×C3 |
| prime radical | C24×C3 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1820 | C3 | direct (N × H) |
| 7. C2×C3×C4⋊C4 | C4 | semidirect |
| 10. C2×C3×C42 | C4 | semidirect |
| 28. C2×C4⋊C4 | C3×C4 | semidirect |
| 31. C2×C42 | C3×C4 | semidirect |
| 94. C3 | #1820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#117 | 2 |
| C3×#381 | 2 |
| C3×#342 | 2 |
| #1820 | 3 |