Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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. #4854 | C2 | direct (N × H) |
| 49. C2×Dic6 | Q8 | semidirect |
| 106. Dic6 | C2×Q8 | semidirect |
| 173. C2×C3 | #475 | semidirect |
| 190. C3 | C2×#475 | semidirect |
| 191. C2 | #4854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#888 | 2 |
| C2×#887 | 2 |
| C2×C3×#106 | 2 |
| C2×#816 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#810 | 2 |
| C2×#808 | 2 |
| #4854 | 2 |
| C2×#475 | 3 |