Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5745 | C2 | semidirect |
| 3. #5132 | C2 | semidirect |
| 4. #5126 | C2 | semidirect |
| 5. #5126 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 34. #344 | D3 | semidirect |
| 58. C2×C3×C8 | D4 | semidirect |
| 70. C2×C3⋊C8 | D4 | semidirect |
| 157. C2×C8 | D12 | semidirect |
| 244. C3 | #1891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5745 | 2 |
| #5524 | 2 |
| #5132 | 2 |
| #5126 | 2 |
| C3×#344 | 2 |
| #4533 | 2 |
| #1891 | 3 |