Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 44. C3×M16 | Q8 | semidirect |
| 60. #208 | Q8 | semidirect |
| 118. M16 | Dic6 | semidirect |
| 191. C3 | #1997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#888 | 2 |
| #5118 | 2 |
| Dic3×M16 | 2 |
| C3×#343 | 2 |
| #4554 | 2 |
| #4530 | 2 |
| #1997 | 3 |