Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 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 |
|---|---|---|
| 3. C3×#365 | C2 | semidirect |
| 4. #4517 | C2 | semidirect |
| 6. #4496 | C2 | semidirect |
| 7. #4487 | C2 | semidirect |
| 23. #365 | D3 | semidirect |
| 119. C3 | #2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4893 | 2 |
| #4867 | 2 |
| C3×#365 | 2 |
| #4517 | 2 |
| #4514 | 2 |
| #4496 | 2 |
| #4487 | 2 |
| #2239 | 3 |