Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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×#500 | C2 | semidirect |
| 4. #5080 | C2 | semidirect |
| 5. #5078 | C2 | semidirect |
| 7. #4876 | C2 | semidirect |
| 9. #4680 | C2 | semidirect |
| 40. #500 | D3 | semidirect |
| 75. ΓL(1,𝔽25) | Q8 | semidirect |
| 121. C3×C8 | C2×Q8 | semidirect |
| 122. C3⋊C8 | C2×Q8 | semidirect |
| 189. C8 | D3×Q8 | semidirect |
| 208. C3 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| D3×C4⋊Q8 | 2 |
| C3×#500 | 2 |
| #5080 | 2 |
| #5078 | 2 |
| #4881 | 2 |
| #4876 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| #4680 | 2 |
| #3165 | 3 |