Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×#918 | C2 | semidirect |
| 2. #5727 | C2 | semidirect |
| 4. C3×#462 | C2 | semidirect |
| 5. #5187 | C2 | semidirect |
| 6. #5085 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4848 | C2 | semidirect |
| 9. #4838 | C2 | semidirect |
| 10. #4812 | C2 | semidirect |
| 11. #4806 | C2 | semidirect |
| 48. #462 | D3 | semidirect |
| 79. #216 | D4 | semidirect |
| 207. C3×C4 | #137 | semidirect |
| 264. C4 | #918 | semidirect |
| 267. C3 | #3278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#918 | 2 |
| #5727 | 2 |
| #5577 | 2 |
| C3×#462 | 2 |
| #5187 | 2 |
| #5085 | 2 |
| C4×#216 | 2 |
| #4848 | 2 |
| #4838 | 2 |
| #4812 | 2 |
| #4806 | 2 |
| #3278 | 3 |