Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#936 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. #5522 | C2 | semidirect |
| 5. C3×#418 | C2 | semidirect |
| 6. #5118 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 8. #4787 | C2 | semidirect |
| 9. #4767 | C2 | semidirect |
| 26. C2×Dic12 | C22 | semidirect |
| 27. C2×#204 | C22 | semidirect |
| 28. #893 | C22 | semidirect |
| 29. #887 | C22 | semidirect |
| 34. Dic3⋊C8 | C22 | semidirect |
| 35. #810 | C22 | semidirect |
| 44. #418 | D3 | semidirect |
| 245. C3 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C2×#932 | 2 |
| C2×#909 | 2 |
| #5522 | 2 |
| C3×#418 | 2 |
| #5118 | 2 |
| #5004 | 2 |
| #4787 | 2 |
| #4767 | 2 |
| #3040 | 3 |