Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
436 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 177 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×C8×Dic3 | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 15. C3×C22⋊C8 | C4 | semidirect |
| 16. #830 | C4 | semidirect |
| 32. C22×Dic3 | C8 | semidirect |
| 37. C2×C3×C8 | C2×C4 | semidirect |
| 43. C2×C3⋊C8 | C2×C4 | semidirect |
| 53. C22⋊C8 | Dic3 | direct (N × H) |
| 96. C2×C8 | C2×Dic3 | semidirect |
| 104. C22×C3 | C4×C8 | semidirect |
| 114. Dic3 | C22⋊C8 | direct (N × H) |
| 149. C22 | C8×Dic3 | semidirect |
| 160. C3 | C4×C22⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic3 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#830 | 2 |
| C2×C8×Dic3 | 2 |
| #4550 | 2 |
| C4×C22⋊C8 | 3 |