Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5557 | C2 | semidirect |
| 2. C3×#442 | C2 | semidirect |
| 4. #5155 | C2 | semidirect |
| 5. #5018 | C2 | semidirect |
| 6. #4867 | C2 | semidirect |
| 7. #4858 | C2 | semidirect |
| 8. #4780 | C2 | semidirect |
| 9. #4768 | C2 | semidirect |
| 10. #4716 | C2 | semidirect |
| 11. #4707 | C2 | semidirect |
| 47. #442 | D3 | semidirect |
| 214. C3 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5557 | 2 |
| C3×#442 | 2 |
| #5159 | 2 |
| #5155 | 2 |
| #5018 | 2 |
| #4867 | 2 |
| #4858 | 2 |
| #4780 | 2 |
| #4768 | 2 |
| #4716 | 2 |
| #4707 | 2 |
| #3183 | 3 |