Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
151 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 151 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. SL(2,𝔽3)⋊C8 | C2 | direct (N × H) |
| 14. C2×SL(2,𝔽3) | C8 | semidirect |
| 36. SL(2,𝔽3) | C2×C8 | semidirect |
| 40. C2×Q8 | C3⋊C8 | semidirect |
| 67. Q8 | C2×C3⋊C8 | semidirect |
| 98. C2 | SL(2,𝔽3)⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)⋊C8 | 2 |
| C2×Q8⋊C8 | 3 |
| C22×C3⋊C8 | 4 |