Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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×#342 | C2 | semidirect |
| 4. #4527 | C2 | semidirect |
| 5. #4526 | C2 | semidirect |
| 9. C22×C4×D3 | C4 | semidirect |
| 15. C2×(C2×D3)⋊C4 | C4 | semidirect |
| 19. D3×C22⋊C4 | C4 | semidirect |
| 24. #342 | D3 | direct (N × H) |
| 35. C22×C3×C4 | C2×C4 | semidirect |
| 37. C22×Dic3 | C2×C4 | semidirect |
| 45. C3×C22⋊C4 | C2×C4 | semidirect |
| 48. #217 | C2×C4 | semidirect |
| 116. C22×C4 | C4×D3 | semidirect |
| 124. C22⋊C4 | C4×D3 | semidirect |
| 196. D3 | #342 | direct (N × H) |
| 225. C3 | C2×#342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C22⋊C4 | 2 |
| C3×#342 | 2 |
| #4527 | 2 |
| #4526 | 2 |
| C2×#342 | 3 |