Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5091 | C2 | semidirect |
| 4. C8×Dic6 | C2 | semidirect |
| 5. #4546 | C2 | semidirect |
| 7. #4457 | C2 | semidirect |
| 148. C3 | #1678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#486 | 2 |
| #5091 | 2 |
| #5075 | 2 |
| C8×Dic6 | 2 |
| #4546 | 2 |
| #4544 | 2 |
| #4457 | 2 |
| #1678 | 3 |