Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4×M16 | C2 | semidirect |
| 4. #5119 | C2 | semidirect |
| 5. C2×#803 | C2 | semidirect |
| 6. #4705 | C2 | semidirect |
| 7. #4690 | C2 | semidirect |
| 30. C4×M16 | D3 | semidirect |
| 150. C3 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C3×C4×M16 | 2 |
| #5129 | 2 |
| #5119 | 2 |
| C2×#803 | 2 |
| #4705 | 2 |
| #4690 | 2 |
| #2923 | 3 |