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 |
|---|---|---|
| 1. C3×#554 | C2 | semidirect |
| 2. #5585 | C2 | semidirect |
| 3. #5091 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. #5068 | C2 | semidirect |
| 6. #5066 | C2 | semidirect |
| 7. Q8×C3⋊C8 | C2 | semidirect |
| 8. C4×#214 | C2 | semidirect |
| 9. #5016 | C2 | semidirect |
| 11. C4×#213 | C2 | semidirect |
| 43. #554 | D3 | semidirect |
| 239. C3 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#554 | 2 |
| #5585 | 2 |
| #5091 | 2 |
| #5088 | 2 |
| #5068 | 2 |
| #5066 | 2 |
| Q8×C3⋊C8 | 2 |
| C4×#214 | 2 |
| #5016 | 2 |
| #5015 | 2 |
| C4×#213 | 2 |
| #3361 | 3 |