Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 4. #4829 | C2 | semidirect |
| 6. #4682 | C2 | semidirect |
| 7. #4681 | C2 | semidirect |
| 8. #4681 | C2 | semidirect |
| 9. #4680 | C2 | semidirect |
| 200. C3 | #3231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×#431 | 2 |
| #4829 | 2 |
| #4723 | 2 |
| #4682 | 2 |
| #4681 | 2 |
| #4680 | 2 |
| #3231 | 3 |