Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5124 | C2 | semidirect |
| 5. #4924 | C2 | semidirect |
| 6. C3×#339 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 21. #805 | C4 | semidirect |
| 22. #805 | C4 | semidirect |
| 30. #339 | D3 | semidirect |
| 189. C3 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5745 | 2 |
| #5124 | 2 |
| #5005 | 2 |
| C2×#805 | 2 |
| #4924 | 2 |
| C3×#339 | 2 |
| #4533 | 2 |
| #1861 | 3 |