Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 8. C2×#208 | C4 | semidirect |
| 9. C22×C3⋊C8 | C4 | semidirect |
| 11. C3×#99 | C4 | semidirect |
| 13. #834 | C4 | semidirect |
| 46. #99 | Dic3 | semidirect |
| 143. C3 | #1391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#410 | 2 |
| #5240 | 2 |
| #5234 | 2 |
| #1391 | 3 |