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 |
|---|---|---|
| 2. #5078 | C2 | semidirect |
| 5. C3×#332 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 7. #4479 | C2 | semidirect |
| 30. #332 | D3 | semidirect |
| 84. C3⋊C8 | SD16 | semidirect |
| 152. C3 | #1673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5083 | 2 |
| #5078 | 2 |
| #4841 | 2 |
| #4834 | 2 |
| C3×#332 | 2 |
| #4486 | 2 |
| #4479 | 2 |
| #1673 | 3 |