Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#830 | C2 | semidirect |
| 8. C22×C3⋊C8 | C22 | semidirect |
| 14. C24×C3 | C8 | semidirect |
| 47. C24 | C3⋊C8 | semidirect |
| 62. C22×C3 | C22⋊C8 | semidirect |
| 92. C22 | #830 | semidirect |
| 98. C3 | #1779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C2×#830 | 2 |
| #1779 | 3 |