Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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. #4505 | C2 | semidirect |
| 5. #4504 | C2 | semidirect |
| 6. #4503 | C2 | semidirect |
| 7. #4503 | C2 | semidirect |
| 126. C3 | #2237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5116 | 2 |
| #5106 | 2 |
| C3×C22⋊C16 | 2 |
| #4505 | 2 |
| #4504 | 2 |
| #4503 | 2 |
| #2237 | 3 |