Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 153. C3 | #2089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5121 | 2 |
| #5119 | 2 |
| #4964 | 2 |
| C2×#807 | 2 |
| C3×#343 | 2 |
| #4558 | 2 |
| #4554 | 2 |
| #2089 | 3 |