Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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×#366 | C2 | semidirect |
| 4. #4504 | C2 | semidirect |
| 5. #4489 | C2 | semidirect |
| 14. D3×C16 | C4 | semidirect |
| 19. #366 | D3 | direct (N × H) |
| 29. C3×C16 | C2×C4 | semidirect |
| 30. C3⋊C16 | C2×C4 | semidirect |
| 60. C16 | C4×D3 | semidirect |
| 84. D3 | #366 | direct (N × H) |
| 94. C3 | C2×#366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C16 | 2 |
| D3×#107 | 2 |
| C3×#366 | 2 |
| #4504 | 2 |
| #4489 | 2 |
| C2×#366 | 3 |