Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#822 | C2 | semidirect |
| 4. #4999 | C2 | semidirect |
| 6. C3×#339 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 21. #810 | C4 | semidirect |
| 22. #810 | C4 | semidirect |
| 23. #809 | C4 | semidirect |
| 24. #809 | C4 | semidirect |
| 33. #339 | D3 | semidirect |
| 212. C3 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#907 | 2 |
| C2×#822 | 2 |
| #5002 | 2 |
| #4999 | 2 |
| C2×#805 | 2 |
| C3×#339 | 2 |
| #4524 | 2 |
| #1866 | 3 |