Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #5584 | C2 | semidirect |
| 3. C3×#460 | C2 | semidirect |
| 4. #5174 | C2 | semidirect |
| 5. #5169 | C2 | semidirect |
| 6. #5070 | C2 | semidirect |
| 7. C4×#215 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4838 | C2 | semidirect |
| 10. #4784 | C2 | semidirect |
| 11. #4770 | C2 | semidirect |
| 15. C2×C3×SD16 | C22 | semidirect |
| 17. C3×C4×Q8 | C22 | semidirect |
| 18. #946 | C22 | semidirect |
| 23. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 25. #892 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 31. C3×C4⋊C8 | C22 | semidirect |
| 32. C3×#102 | C22 | semidirect |
| 33. #835 | C22 | semidirect |
| 34. #832 | C22 | semidirect |
| 35. #832 | C22 | semidirect |
| 37. (C2×D3)⋊C8 | C22 | semidirect |
| 38. #818 | C22 | semidirect |
| 40. #808 | C22 | semidirect |
| 41. C4×C3⋊C8 | C22 | semidirect |
| 48. #460 | D3 | semidirect |
| 92. C2×SD16 | C2×D3 | semidirect |
| 103. C4×Q8 | C2×D3 | semidirect |
| 109. C4⋊C8 | C2×D3 | semidirect |
| 115. #102 | C2×D3 | semidirect |
| 264. C3 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5717 | 2 |
| #5584 | 2 |
| C3×#460 | 2 |
| #5174 | 2 |
| #5169 | 2 |
| #5070 | 2 |
| C4×#215 | 2 |
| #4846 | 2 |
| #4838 | 2 |
| #4784 | 2 |
| #4770 | 2 |
| #3324 | 3 |