Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. C3×#419 | C2 | semidirect |
| 4. C2×#836 | C2 | semidirect |
| 6. C3⋊#338 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 13. C2×#216 | C4 | semidirect |
| 16. C2×#215 | C4 | semidirect |
| 29. #419 | D3 | semidirect |
| 209. C3 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#942 | 2 |
| #5745 | 2 |
| C3×#419 | 2 |
| C2×#836 | 2 |
| #5005 | 2 |
| C3⋊#338 | 2 |
| #4533 | 2 |
| #1902 | 3 |