Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 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. #4851 | C2 | semidirect |
| 4. #4679 | C2 | semidirect |
| 5. C3×#335 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 28. #335 | D3 | semidirect |
| 84. C3×C8 | SD16 | semidirect |
| 137. C8 | #204 | semidirect |
| 154. C3 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4851 | 2 |
| #4848 | 2 |
| #4693 | 2 |
| #4679 | 2 |
| C3×#335 | 2 |
| #4486 | 2 |
| #4485 | 2 |
| #1686 | 3 |