Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 8. #4856 | C2 | direct (N × H) |
| 47. C2×C3×C8 | Q8 | semidirect |
| 62. C2×C3⋊C8 | Q8 | semidirect |
| 102. C3×C8 | C2×Q8 | semidirect |
| 103. C3⋊C8 | C2×Q8 | semidirect |
| 115. C2×C8 | Dic6 | semidirect |
| 162. C8 | C2×Dic6 | semidirect |
| 163. C2×C3 | #501 | semidirect |
| 180. C3 | C2×#501 | semidirect |
| 181. C2 | #4856 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#890 | 2 |
| C2×#888 | 2 |
| C2×C3×#106 | 2 |
| C2×#818 | 2 |
| C2×#815 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| #4856 | 2 |
| C2×#501 | 3 |