Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. #5070 | C2 | semidirect |
| 3. #5012 | C2 | semidirect |
| 4. #5008 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. #4481 | C2 | semidirect |
| 7. #4479 | C2 | semidirect |
| 159. C3 | #1697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#459 | 2 |
| #5070 | 2 |
| #5012 | 2 |
| #5008 | 2 |
| #4544 | 2 |
| #4481 | 2 |
| #4479 | 2 |
| #1697 | 3 |