Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 4. #4699 | C2 | semidirect |
| 5. C4×Dic12 | C2 | semidirect |
| 6. #4682 | C2 | semidirect |
| 7. #4681 | C2 | semidirect |
| 72. C2×C3×C4 | Q16 | semidirect |
| 125. C2×C4 | Dic12 | semidirect |
| 150. C3 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C2×C3×C4×C8 | 2 |
| #5116 | 2 |
| #4699 | 2 |
| C4×Dic12 | 2 |
| #4682 | 2 |
| #4681 | 2 |
| #3170 | 3 |