Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 89 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×#568 | C2 | semidirect |
| 3. #5237 | C2 | semidirect |
| 4. #5126 | C2 | semidirect |
| 5. #4556 | C2 | semidirect |
| 22. #568 | D3 | semidirect |
| 45. C2×C3×C8 | D4 | semidirect |
| 115. C2×C8 | #67 | semidirect |
| 183. C3 | #1891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568 | 2 |
| #5828 | 2 |
| #5237 | 2 |
| #5126 | 2 |
| #4556 | 2 |
| #1891 | 3 |