Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 184 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 |
|---|---|---|
| 1. #4848 | C2 | semidirect |
| 3. #4679 | C2 | semidirect |
| 4. C3×#334 | C2 | semidirect |
| 5. #4485 | C2 | semidirect |
| 21. #334 | D3 | semidirect |
| 63. C3×C8 | SD16 | semidirect |
| 105. C8 | #204 | semidirect |
| 120. C3 | #1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4848 | 2 |
| #4695 | 2 |
| #4679 | 2 |
| C3×#334 | 2 |
| #4485 | 2 |
| #1688 | 3 |