Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
149 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 149 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | S4 |
| commutator, hypocenter | SL(2,𝔽3) | C42 |
| Frattini | C2×C4 | C2×S4 |
| Fitting | C2×#131 | D3 |
| socle | C22 | C4×S4 |
| prime radical, cosocle | C2×#41⋊C3 | C22 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #131⋊C3 | C4 | semidirect |
| 7. GU(2,𝔽3) | C4 | semidirect |
| 8. #859 | C4 | semidirect |
| 25. #131 | Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#131⋊C3 | 2 |
| #5424 | 2 |
| C2×GU(2,𝔽3) | 2 |
| #1764 | 3 |
| C8×Dic3 | 4 |