Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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. #5119 | C2 | semidirect |
| 5. #4556 | C2 | semidirect |
| 126. C3 | #1868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568 | 2 |
| #5240 | 2 |
| #5234 | 2 |
| #5119 | 2 |
| #4556 | 2 |
| #1868 | 3 |