Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C3×#498 | C2 | semidirect |
| 3. #5093 | C2 | semidirect |
| 5. #4853 | C2 | semidirect |
| 6. #4699 | C2 | semidirect |
| 26. #498 | D3 | semidirect |
| 133. C3 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C3×#498 | 2 |
| #5093 | 2 |
| #4867 | 2 |
| #4853 | 2 |
| #4699 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| #3185 | 3 |