Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5137 | C2 | semidirect |
| 4. #5116 | C2 | semidirect |
| 5. #4739 | C2 | semidirect |
| 6. #4723 | C2 | semidirect |
| 166. C3 | #3202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5825 | 2 |
| C3×#408 | 2 |
| #5137 | 2 |
| #5116 | 2 |
| #4739 | 2 |
| #4723 | 2 |
| #3202 | 3 |