Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. C2×#869 | C2 | semidirect |
| 3. #5064 | C2 | semidirect |
| 4. #5055 | C2 | semidirect |
| 5. #5044 | C2 | semidirect |
| 7. #5020 | C2 | semidirect |
| 8. #5007 | C2 | semidirect |
| 9. #4926 | C2 | semidirect |
| 219. C3 | #3239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#529 | 2 |
| C2×#869 | 2 |
| #5064 | 2 |
| #5055 | 2 |
| #5044 | 2 |
| #5034 | 2 |
| #5020 | 2 |
| #5007 | 2 |
| #4926 | 2 |
| #3239 | 3 |