Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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×#501 | C2 | semidirect |
| 4. #5081 | C2 | semidirect |
| 5. #5064 | C2 | semidirect |
| 7. #4878 | C2 | semidirect |
| 9. #4858 | C2 | semidirect |
| 11. #4702 | C2 | semidirect |
| 49. #501 | D3 | semidirect |
| 90. ΓL(1,𝔽25) | Q8 | semidirect |
| 238. C3 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| D3×#125 | 2 |
| C3×#501 | 2 |
| #5081 | 2 |
| #5064 | 2 |
| #4881 | 2 |
| #4878 | 2 |
| #4861 | 2 |
| #4858 | 2 |
| #4707 | 2 |
| #4702 | 2 |
| #3166 | 3 |