Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 3. #5091 | C2 | semidirect |
| 4. #5088 | C2 | semidirect |
| 5. #5049 | C2 | semidirect |
| 6. #5047 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #5027 | C2 | semidirect |
| 9. #5012 | C2 | semidirect |
| 10. #4967 | C2 | semidirect |
| 11. #4966 | C2 | semidirect |
| 42. #554 | D3 | semidirect |
| 251. C3 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#554 | 2 |
| #5553 | 2 |
| #5091 | 2 |
| #5088 | 2 |
| #5049 | 2 |
| #5047 | 2 |
| C4×#216 | 2 |
| #5027 | 2 |
| #5012 | 2 |
| #4967 | 2 |
| #4966 | 2 |
| #3333 | 3 |