Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #5500 | C2 | semidirect |
| 5. #5106 | C2 | semidirect |
| 6. #5102 | C2 | semidirect |
| 7. #4964 | C2 | semidirect |
| 8. #4766 | C2 | semidirect |
| 9. #4763 | C2 | semidirect |
| 10. #4761 | C2 | semidirect |
| 11. #4759 | C2 | semidirect |
| 27. #890 | C22 | semidirect |
| 29. #888 | C22 | semidirect |
| 34. #818 | C22 | semidirect |
| 35. #818 | C22 | semidirect |
| 36. #817 | C22 | semidirect |
| 37. #817 | C22 | semidirect |
| 38. Dic3⋊C8 | C22 | semidirect |
| 39. Dic3⋊C8 | C22 | semidirect |
| 40. #808 | C22 | semidirect |
| 41. #807 | C22 | semidirect |
| 56. C2×C3×D4 | Q8 | semidirect |
| 146. C2×D4 | Dic6 | semidirect |
| 243. C3 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5798 | 2 |
| #5500 | 2 |
| C2×C3×#102 | 2 |
| #5215 | 2 |
| #5106 | 2 |
| #5102 | 2 |
| #4964 | 2 |
| #4766 | 2 |
| #4763 | 2 |
| #4761 | 2 |
| #4759 | 2 |
| #3081 | 3 |