Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #5470 | C2 | semidirect |
| 3. #5080 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 5. #5070 | C2 | semidirect |
| 6. #5070 | C2 | semidirect |
| 7. #5035 | C2 | semidirect |
| 8. #5009 | C2 | semidirect |
| 9. #4925 | C2 | semidirect |
| 215. C3 | #3228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #5470 | 2 |
| #5080 | 2 |
| #5078 | 2 |
| #5070 | 2 |
| #5035 | 2 |
| #5009 | 2 |
| #4925 | 2 |
| #3228 | 3 |