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. #5119 | C2 | direct (N × H) |
| 5. C2×Dic3⋊C8 | C2 | semidirect |
| 19. Dic3⋊C8 | C22 | semidirect |
| 120. C2×C3 | #424 | semidirect |
| 134. C3 | C2×#424 | semidirect |
| 136. C2 | #5119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| C2×#926 | 2 |
| C23×C3⋊C8 | 2 |
| #5119 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#424 | 3 |