Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
752 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 752 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. #5120 | C2 | direct (N × H) |
| 5. C2×#816 | C2 | semidirect |
| 12. C22×Dic6 | C4 | semidirect |
| 23. #816 | C22 | semidirect |
| 47. C2×Dic6 | C2×C4 | semidirect |
| 159. C2×C3 | #419 | semidirect |
| 174. C3 | C2×#419 | semidirect |
| 176. C2 | #5120 | 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 |
| C2×#926 | 2 |
| #5120 | 2 |
| C2×#816 | 2 |
| C2×#419 | 3 |