Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#822 | C2 | semidirect |
| 5. #5122 | C2 | semidirect |
| 6. #4524 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 17. #835 | C4 | semidirect |
| 18. #835 | C4 | semidirect |
| 19. #832 | C4 | semidirect |
| 20. #832 | C4 | semidirect |
| 204. C3 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#104 | 2 |
| #5234 | 2 |
| #5233 | 2 |
| C2×#822 | 2 |
| #5122 | 2 |
| #4524 | 2 |
| #4523 | 2 |
| #1929 | 3 |