Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 4. C2×#824 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. C3⋊#338 | C2 | semidirect |
| 7. #4559 | C2 | semidirect |
| 18. C2×#216 | C4 | semidirect |
| 19. C2×#214 | C4 | semidirect |
| 209. C3 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568 | 2 |
| C2×#951 | 2 |
| #5236 | 2 |
| C2×#824 | 2 |
| #5120 | 2 |
| C3⋊#338 | 2 |
| #4559 | 2 |
| #1902 | 3 |