Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 38. C3×C16 | Q8 | semidirect |
| 39. C3⋊C16 | Q8 | semidirect |
| 74. C16 | Dic6 | semidirect |
| 107. C3 | #2255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4878 | 2 |
| #4874 | 2 |
| C3×#367 | 2 |
| #4504 | 2 |
| #4502 | 2 |
| #4490 | 2 |
| #4489 | 2 |
| #2255 | 3 |