Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
432 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #4530 | C2 | direct (N × H) |
| 13. C2×#208 | C4 | semidirect |
| 35. #208 | C2×C4 | semidirect |
| 134. C2×C3 | #343 | semidirect |
| 155. C3 | C2×#343 | semidirect |
| 159. C2 | #4530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C22×#208 | 2 |
| #4530 | 2 |
| C2×#343 | 3 |