Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. #4893 | C2 | semidirect |
| 3. C3×#365 | C2 | semidirect |
| 4. #4516 | C2 | semidirect |
| 5. #4514 | C2 | semidirect |
| 6. #4495 | C2 | semidirect |
| 7. #4487 | C2 | semidirect |
| 23. #365 | D3 | semidirect |
| 126. C3 | #2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4893 | 2 |
| #4865 | 2 |
| C3×#365 | 2 |
| #4516 | 2 |
| #4514 | 2 |
| #4495 | 2 |
| #4487 | 2 |
| #2238 | 3 |