Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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. #4998 | C2 | direct (N × H) |
| 5. C2×#808 | C2 | semidirect |
| 6. C2×#807 | C2 | semidirect |
| 19. C22×C3⋊C8 | C4 | semidirect |
| 23. #808 | C22 | semidirect |
| 24. #807 | C22 | semidirect |
| 50. C2×C3⋊C8 | C2×C4 | semidirect |
| 143. C2×C3 | #427 | semidirect |
| 158. C3 | C2×#427 | semidirect |
| 160. C2 | #4998 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#117 | 2 |
| C2×#926 | 2 |
| C23×C3⋊C8 | 2 |
| #4998 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| C2×#427 | 3 |