Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #5728 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. #5070 | C2 | semidirect |
| 6. #4770 | C2 | semidirect |
| 7. #4764 | C2 | semidirect |
| 8. #4694 | C2 | semidirect |
| 9. C4×ΓL(1,𝔽25) | C2 | semidirect |
| 14. C3×C4⋊Q8 | C22 | semidirect |
| 24. #890 | C22 | semidirect |
| 28. #869 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. C3×C4×C8 | C22 | semidirect |
| 31. #832 | C22 | semidirect |
| 32. #821 | C22 | semidirect |
| 33. #815 | C22 | semidirect |
| 34. #809 | C22 | semidirect |
| 35. C4×C3⋊C8 | C22 | semidirect |
| 42. #486 | D3 | semidirect |
| 83. C4⋊Q8 | C2×D3 | semidirect |
| 99. #102 | C2×D3 | semidirect |
| 102. C4×C8 | C2×D3 | semidirect |
| 240. C3 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| D3×#127 | 2 |
| C3×#486 | 2 |
| #5088 | 2 |
| #5070 | 2 |
| #4770 | 2 |
| #4764 | 2 |
| #4694 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| #3138 | 3 |