Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 284 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. #4473 | C2 | direct (N × H) |
| 7. C22×Dic6 | C4 | semidirect |
| 14. #936 | C4 | semidirect |
| 16. C2×C4×Dic3 | C4 | semidirect |
| 41. C2×Dic6 | C2×C4 | semidirect |
| 51. C4×Dic3 | C2×C4 | semidirect |
| 182. C2×C3 | #354 | semidirect |
| 206. C3 | C2×#354 | semidirect |
| 213. C2 | #4473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| #4473 | 2 |
| C2×#354 | 3 |