Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. #5518 | C2 | semidirect |
| 4. #5019 | C2 | semidirect |
| 5. #5018 | C2 | semidirect |
| 6. C4×#214 | C2 | semidirect |
| 7. #5009 | C2 | semidirect |
| 8. #5000 | C2 | semidirect |
| 9. #4996 | C2 | semidirect |
| 23. #870 | C22 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. C4×Dic6 | C22 | semidirect |
| 29. #810 | C22 | semidirect |
| 30. #810 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 32. #807 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 34. #803 | C22 | semidirect |
| 35. C4×C3⋊C8 | C22 | semidirect |
| 200. C3 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#518 | 2 |
| #5518 | 2 |
| #5218 | 2 |
| #5019 | 2 |
| #5018 | 2 |
| C4×#214 | 2 |
| #5009 | 2 |
| #5000 | 2 |
| #4996 | 2 |
| #3123 | 3 |