Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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×#533 | C2 | semidirect |
| 3. #5094 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 5. #5087 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 8. #5045 | C2 | semidirect |
| 9. C4×#216 | C2 | semidirect |
| 10. C4×#215 | C2 | semidirect |
| 11. #4925 | C2 | semidirect |
| 44. #533 | D3 | semidirect |
| 267. C3 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C4×#235 | 2 |
| #5094 | 2 |
| #5090 | 2 |
| #5087 | 2 |
| #5083 | 2 |
| #5047 | 2 |
| #5045 | 2 |
| C4×#216 | 2 |
| C4×#215 | 2 |
| #4925 | 2 |
| #3107 | 3 |