Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. #5094 | C2 | semidirect |
| 4. #4679 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 7. #4458 | C2 | semidirect |
| 82. C3×C8 | SD16 | semidirect |
| 137. C8 | #214 | semidirect |
| 154. C3 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#492 | 2 |
| #5094 | 2 |
| #5075 | 2 |
| #4679 | 2 |
| #4547 | 2 |
| #4544 | 2 |
| #4458 | 2 |
| #1686 | 3 |