Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. C22×#216 | C2 | semidirect |
| 4. C2×C4×Dic6 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 7. #5054 | C2 | direct (N × H) |
| 8. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 19. C2×#216 | C22 | semidirect |
| 28. C4×Dic6 | C22 | semidirect |
| 29. #835 | C22 | semidirect |
| 31. C4⋊(C3⋊C8) | C22 | semidirect |
| 205. C2×C3 | #464 | semidirect |
| 225. C3 | C2×#464 | semidirect |
| 227. C2 | #5054 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#124 | 2 |
| C22×#216 | 2 |
| C22×#214 | 2 |
| C2×C4×Dic6 | 2 |
| C2×#835 | 2 |
| C2×#832 | 2 |
| #5054 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#464 | 3 |