Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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. #4476 | C2 | direct (N × H) |
| 7. C23×Dic3 | C4 | semidirect |
| 11. C2×#217 | C4 | semidirect |
| 14. #935 | C4 | semidirect |
| 40. C22×Dic3 | C2×C4 | semidirect |
| 49. #217 | C2×C4 | semidirect |
| 179. C2×C3 | #352 | semidirect |
| 202. C3 | C2×#352 | semidirect |
| 209. C2 | #4476 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#935 | 2 |
| C2×C3×#100 | 2 |
| C2×#834 | 2 |
| #4476 | 2 |
| C2×#352 | 3 |