Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. C3×#391 | C2 | semidirect |
| 4. #5225 | C2 | semidirect |
| 6. #4530 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 15. #942 | C4 | semidirect |
| 33. #391 | D3 | semidirect |
| 41. C2×C3×Q8 | C2×C4 | semidirect |
| 71. #208 | C2×C4 | semidirect |
| 138. C2×Q8 | C4×D3 | semidirect |
| 242. C3 | #1882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#942 | 2 |
| #5504 | 2 |
| C3×#391 | 2 |
| #5225 | 2 |
| C2×#805 | 2 |
| #4530 | 2 |
| #4523 | 2 |
| #1882 | 3 |