Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
358 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 133 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. #4716 | C2 | semidirect |
| 5. #4699 | C2 | semidirect |
| 6. #4681 | C2 | semidirect |
| 7. #4680 | C2 | semidirect |
| 133. C3 | #3185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×C4×M16 | 2 |
| #5137 | 2 |
| #4716 | 2 |
| #4699 | 2 |
| #4681 | 2 |
| #4680 | 2 |
| #3185 | 3 |