Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
736 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×#824 | C2 | direct (N × H) |
| 20. #824 | C22 | direct (N × H) |
| 114. C22×C3 | #101 | semidirect |
| 147. C2×C3 | C2×#101 | semidirect |
| 151. C22 | #824 | direct (N × H) |
| 160. C3 | C22×#101 | semidirect |
| 163. C2 | C2×#824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C22×C3×M16 | 2 |
| C22×#208 | 2 |
| C2×#824 | 2 |
| C22×#101 | 3 |