Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 402 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. #5088 | C2 | semidirect |
| 4. #5085 | C2 | semidirect |
| 5. #5079 | C2 | semidirect |
| 6. #5078 | C2 | semidirect |
| 7. #5049 | C2 | semidirect |
| 8. #5026 | C2 | semidirect |
| 9. C4×#208 | C2 | semidirect |
| 36. #533 | D3 | semidirect |
| 125. C3⋊C8 | #41 | semidirect |
| 219. C3 | #3182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| #5477 | 2 |
| #5088 | 2 |
| #5085 | 2 |
| #5079 | 2 |
| #5078 | 2 |
| #5049 | 2 |
| #5026 | 2 |
| C4×#208 | 2 |
| #3182 | 3 |