Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 4. C3×#328 | C2 | semidirect |
| 5. #4538 | C2 | semidirect |
| 6. #4467 | C2 | semidirect |
| 7. #4452 | C2 | semidirect |
| 9. C2×D3×Q8 | C4 | semidirect |
| 13. #946 | C4 | semidirect |
| 16. #897 | C4 | semidirect |
| 19. D3×C4⋊C4 | C4 | semidirect |
| 34. #328 | D3 | direct (N × H) |
| 36. C2×C3×Q8 | C2×C4 | semidirect |
| 53. C2×Dic6 | C2×C4 | semidirect |
| 56. C3×C4⋊C4 | C2×C4 | semidirect |
| 62. C4⋊Dic3 | C2×C4 | semidirect |
| 126. C2×Q8 | C4×D3 | semidirect |
| 150. C4⋊C4 | C4×D3 | semidirect |
| 219. D3 | #328 | direct (N × H) |
| 243. C3 | C2×#328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C22⋊Q8 | 2 |
| D3×C22⋊C8 | 2 |
| D3×#95 | 2 |
| C3×#328 | 2 |
| #4538 | 2 |
| #4467 | 2 |
| #4452 | 2 |
| C2×#328 | 3 |