Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. D3×C22⋊C8 | C2 | semidirect |
| 3. #4664 | C2 | semidirect |
| 4. C3×#327 | C2 | semidirect |
| 5. #4537 | C2 | semidirect |
| 6. #4467 | C2 | semidirect |
| 7. #4452 | C2 | semidirect |
| 9. C2×#237 | C4 | semidirect |
| 12. #938 | C4 | semidirect |
| 18. #897 | C4 | semidirect |
| 19. #892 | C4 | semidirect |
| 34. #327 | D3 | semidirect |
| 246. C3 | #1516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5606 | 2 |
| D3×C22⋊C8 | 2 |
| #4664 | 2 |
| C3×#327 | 2 |
| #4537 | 2 |
| #4467 | 2 |
| #4452 | 2 |
| #1516 | 3 |