Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5563 | C2 | semidirect |
| 2. #5553 | C2 | semidirect |
| 3. C3×C8×D4 | C2 | semidirect |
| 4. #5115 | C2 | semidirect |
| 5. #5113 | C2 | semidirect |
| 6. #4850 | C2 | semidirect |
| 7. #4843 | C2 | semidirect |
| 8. #4737 | C2 | semidirect |
| 9. #4734 | C2 | semidirect |
| 10. #4694 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 51. C8×D4 | D3 | semidirect |
| 258. C3 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5563 | 2 |
| #5553 | 2 |
| C3×C8×D4 | 2 |
| #5115 | 2 |
| #5113 | 2 |
| #4850 | 2 |
| #4843 | 2 |
| #4737 | 2 |
| #4734 | 2 |
| #4694 | 2 |
| C4×#204 | 2 |
| #3305 | 3 |