Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5730 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5075 | C2 | semidirect |
| 6. #4783 | C2 | semidirect |
| 7. #4780 | C2 | semidirect |
| 8. #4774 | C2 | semidirect |
| 9. #4771 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 44. #486 | D3 | semidirect |
| 251. C3 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5718 | 2 |
| C3×#486 | 2 |
| #5091 | 2 |
| #5075 | 2 |
| #4783 | 2 |
| #4780 | 2 |
| #4774 | 2 |
| #4771 | 2 |
| C4×Dic12 | 2 |
| #4688 | 2 |
| #3333 | 3 |