Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 32 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 |
|---|---|---|
| 5. C4×SL(2,𝔽3) | C4 | semidirect |
| 6. C4×SL(2,𝔽3) | C4 | semidirect |
| 37. SL(2,𝔽3) | C4⋊C4 | semidirect |
| 103. C4 | GU(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41⋊C3 | 2 |
| C2×GU(2,𝔽3) | 2 |
| #1806 | 3 |
| C4⋊(C3⋊C8) | 4 |