Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #5519 | C2 | semidirect |
| 5. #5009 | C2 | semidirect |
| 6. #5009 | C2 | semidirect |
| 7. #5008 | C2 | semidirect |
| 8. #5007 | C2 | semidirect |
| 9. #4999 | C2 | semidirect |
| 10. #4998 | C2 | semidirect |
| 11. #4995 | C2 | semidirect |
| 28. #870 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 34. #808 | C22 | semidirect |
| 35. #808 | C22 | semidirect |
| 36. #808 | C22 | semidirect |
| 37. #807 | C22 | semidirect |
| 38. #807 | C22 | semidirect |
| 39. #807 | C22 | semidirect |
| 40. C4⋊(C3⋊C8) | C22 | semidirect |
| 41. C4⋊(C3⋊C8) | 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 |
|---|---|
| C3×#518 | 2 |
| #5519 | 2 |
| #5215 | 2 |
| C2×#832 | 2 |
| #5009 | 2 |
| #5008 | 2 |
| #5007 | 2 |
| #4999 | 2 |
| #4998 | 2 |
| #4995 | 2 |
| #3081 | 3 |