Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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×#495 | C2 | semidirect |
| 2. #5179 | C2 | semidirect |
| 4. #4700 | C2 | semidirect |
| 5. #4565 | C2 | semidirect |
| 6. #4563 | C2 | semidirect |
| 7. #4463 | C2 | semidirect |
| 26. #495 | D3 | semidirect |
| 144. C3 | #2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#495 | 2 |
| #5179 | 2 |
| #5147 | 2 |
| #4700 | 2 |
| #4565 | 2 |
| #4563 | 2 |
| #4463 | 2 |
| #2212 | 3 |