Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
135 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 1. Q8×SL(2,𝔽3) | C2 | semidirect |
| 3. C8×SL(2,𝔽3) | C2 | semidirect |
| 4. Q8×SD16 | C3 | semidirect |
| 9. Q82 | C2×C3 | semidirect |
| 14. C8×Q8 | C2×C3 | semidirect |
| 45. SL(2,𝔽3) | SD16 | direct (N × H) |
| 55. SD16 | SL(2,𝔽3) | direct (N × H) |
| 80. Q8 | C3×SD16 | semidirect |
| 81. Q8 | C2×SL(2,𝔽3) | semidirect |
| 93. C8 | C2×SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×SL(2,𝔽3) | 2 |
| D4×SL(2,𝔽3) | 2 |
| C8×SL(2,𝔽3) | 2 |
| Q8×SD16 | 3 |
| C2×C3×SD16 | 4 |