Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
217 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 3. #5391 | C2 | semidirect |
| 4. #5386 | C2 | semidirect |
| 21. #41⋊C3 | Q8 | semidirect |
| 52. SL(2,𝔽3) | C2×Q8 | semidirect |
| 54. #41 | Dic6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41⋊C3 | 2 |
| #5426 | 2 |
| #5391 | 2 |
| #5386 | 2 |
| #3079 | 3 |
| #869 | 4 |