Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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×C3×#127 | C2 | semidirect |
| 2. #5479 | C2 | semidirect |
| 3. #5218 | C2 | semidirect |
| 4. #5217 | C2 | semidirect |
| 5. #5075 | C2 | semidirect |
| 6. #5074 | C2 | semidirect |
| 7. #5072 | C2 | semidirect |
| 8. #5071 | C2 | semidirect |
| 9. #4926 | C2 | semidirect |
| 19. C2×#214 | C22 | semidirect |
| 20. C2×#213 | C22 | semidirect |
| 26. #875 | C22 | semidirect |
| 27. C4×D12 | C22 | semidirect |
| 29. #870 | C22 | semidirect |
| 30. C4×Dic6 | C22 | semidirect |
| 31. #832 | C22 | semidirect |
| 32. #832 | C22 | semidirect |
| 34. C4⋊(C3⋊C8) | C22 | semidirect |
| 35. #803 | C22 | semidirect |
| 36. C2×#127 | D3 | semidirect |
| 248. C3 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| #5479 | 2 |
| #5218 | 2 |
| #5217 | 2 |
| #5075 | 2 |
| #5074 | 2 |
| #5072 | 2 |
| #5071 | 2 |
| #4926 | 2 |
| #3217 | 3 |