Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 1. #5094 | C2 | semidirect |
| 4. #4830 | C2 | semidirect |
| 5. C3×#332 | C2 | semidirect |
| 7. #4480 | C2 | semidirect |
| 29. #332 | D3 | semidirect |
| 80. Dic6 | SD16 | semidirect |
| 85. C3⋊C8 | SD16 | semidirect |
| 154. C3 | #1666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5094 | 2 |
| #5085 | 2 |
| #4848 | 2 |
| #4830 | 2 |
| C3×#332 | 2 |
| #4485 | 2 |
| #4480 | 2 |
| #1666 | 3 |