Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
263 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 46 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) | C22×C4 |
| Frattini | C4 | C22×S4 |
| Fitting | C2×#131 | D3 |
| socle | C22 | C4×S4 |
| prime radical | C2×#985 | C2 |
| cosocle | #41⋊C3 | C23 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#131⋊C3 | C2 | semidirect |
| 3. C2×GU(2,𝔽3) | C2 | semidirect |
| 4. #5404 | C2 | direct (N × H) |
| 7. #985 | C4 | semidirect |
| 9. C2×GL(2,𝔽3) | C4 | semidirect |
| 10. C2×#226 | C4 | semidirect |
| 12. #131⋊C3 | C22 | semidirect |
| 13. GU(2,𝔽3) | C22 | semidirect |
| 16. C2×#131 | D3 | semidirect |
| 27. GL(2,𝔽3) | C2×C4 | semidirect |
| 28. #226 | C2×C4 | semidirect |
| 45. #131 | C2×D3 | semidirect |
| 161. C2 | #5404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#985 | 2 |
| C2×#131⋊C3 | 2 |
| C2×GU(2,𝔽3) | 2 |
| #5404 | 2 |
| C2×#443 | 3 |
| C2×D3×C8 | 4 |