Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
112 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 24 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. C8×SL(2,𝔽3) | C2 | semidirect |
| 3. SL(2,𝔽3)⋊C8 | C2 | semidirect |
| 9. C8×Q8 | D3 | semidirect |
| 18. GL(2,𝔽3) | C8 | semidirect |
| 39. SL(2,𝔽3) | C2×C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×GL(2,𝔽3) | 2 |
| C8×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)⋊C8 | 2 |
| SD16⋊C8 | 3 |
| (C2×D3)⋊C8 | 4 |