Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. C3×D4×Q8 | C2 | semidirect |
| 3. #5227 | C2 | semidirect |
| 4. #5225 | C2 | semidirect |
| 5. #5083 | C2 | semidirect |
| 6. #5079 | C2 | semidirect |
| 7. #5049 | C2 | semidirect |
| 8. #5045 | C2 | semidirect |
| 9. C4×#215 | C2 | semidirect |
| 10. #5021 | C2 | semidirect |
| 11. #5012 | C2 | semidirect |
| 43. D4×Q8 | D3 | semidirect |
| 247. C3 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Q8 | 2 |
| #5563 | 2 |
| #5227 | 2 |
| #5225 | 2 |
| #5083 | 2 |
| #5079 | 2 |
| #5049 | 2 |
| #5045 | 2 |
| C4×#215 | 2 |
| #5021 | 2 |
| #5012 | 2 |
| #3329 | 3 |