Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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. C3×C8×Q8 | C2 | semidirect |
| 2. #5031 | C2 | semidirect |
| 5. #4486 | C2 | semidirect |
| 7. #4458 | C2 | semidirect |
| 27. C8×Q8 | D3 | semidirect |
| 152. C3 | #1682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| #5031 | 2 |
| #5027 | 2 |
| #4694 | 2 |
| #4486 | 2 |
| #4485 | 2 |
| #4458 | 2 |
| #1682 | 3 |