Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C3×#430 | C2 | semidirect |
| 5. #5125 | C2 | semidirect |
| 6. #5124 | C2 | semidirect |
| 7. C3⋊#338 | C2 | semidirect |
| 24. #430 | D3 | semidirect |
| 165. C3 | #2069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#430 | 2 |
| C2×#823 | 2 |
| #5125 | 2 |
| #5124 | 2 |
| C3⋊#338 | 2 |
| #2069 | 3 |