Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 43 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. #5155 | C2 | semidirect |
| 3. #4909 | C2 | semidirect |
| 4. #4895 | C2 | semidirect |
| 5. C3×#361 | C2 | semidirect |
| 6. #4511 | C2 | semidirect |
| 7. #4496 | C2 | semidirect |
| 30. #361 | 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 |
|---|---|
| #5155 | 2 |
| #5147 | 2 |
| #4909 | 2 |
| #4895 | 2 |
| C3×#361 | 2 |
| #4511 | 2 |
| #4496 | 2 |
| #2212 | 3 |