Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×S4 |
| commutator, hypocenter | SL(2,𝔽3) | C22×C4 |
| Frattini, socle | C22 | C22×S4 |
| Fitting | C4×#41 | D3 |
| prime radical | C2×#41⋊C3 | C22 |
| cosocle | C2×SL(2,𝔽3) | C23 |
| hypercenter | C42 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #5388 | C2 | semidirect |
| 5. C4×#226 | C2 | semidirect |
| 8. #984 | C4 | direct (N × H) |
| 28. #226 | C2×C4 | semidirect |
| 147. C4 | #984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#984 | 2 |
| C4×#41⋊C3 | 2 |
| #5426 | 2 |
| #5388 | 2 |
| C4×#226 | 2 |
| C4×#137 | 3 |
| C4×Dic6 | 4 |