Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 73 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. #4997 | C2 | semidirect |
| 6. C3×#339 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 19. #810 | C4 | semidirect |
| 20. #810 | C4 | semidirect |
| 21. #809 | C4 | semidirect |
| 22. #809 | C4 | semidirect |
| 31. #339 | D3 | semidirect |
| 204. C3 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5129 | 2 |
| C2×#822 | 2 |
| #5002 | 2 |
| #4997 | 2 |
| C2×#805 | 2 |
| C3×#339 | 2 |
| #4524 | 2 |
| #1929 | 3 |