Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 13. #870 | C4 | semidirect |
| 14. #869 | C4 | semidirect |
| 15. #869 | C4 | semidirect |
| 32. C3×M16 | Q8 | semidirect |
| 89. M16 | Dic6 | semidirect |
| 157. C3 | #1986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×C4×M16 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4555 | 2 |
| #1986 | 3 |