Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
313 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5423 | C2 | direct (N × H) |
| 3. C2×GU(2,𝔽3) | C2 | semidirect |
| 5. C2×#41⋊C3 | C4 | semidirect |
| 6. C2×#41⋊C3 | C4 | semidirect |
| 9. C22×SL(2,𝔽3) | C4 | semidirect |
| 11. GU(2,𝔽3) | C22 | semidirect |
| 21. #41⋊C3 | C2×C4 | semidirect |
| 24. C2×SL(2,𝔽3) | C2×C4 | semidirect |
| 171. C2 | #5423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41⋊C3 | 2 |
| #5423 | 2 |
| C2×GU(2,𝔽3) | 2 |
| C2×#421 | 3 |
| C2×#208 | 4 |