Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 4. #5020 | C2 | direct (N × H) |
| 32. C2×C3×Q8 | Q8 | semidirect |
| 72. C3×Q8 | C2×Q8 | semidirect |
| 93. C2×Q8 | Dic6 | semidirect |
| 128. Q8 | C2×Dic6 | semidirect |
| 144. C2×C3 | #475 | semidirect |
| 160. C3 | C2×#475 | semidirect |
| 161. C2 | #5020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Q8 | 2 |
| C2×#869 | 2 |
| C2×#835 | 2 |
| #5020 | 2 |
| C2×#808 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#475 | 3 |