Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 123. C3 | #2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5183 | 2 |
| #4878 | 2 |
| C3×#358 | 2 |
| #4564 | 2 |
| #4503 | 2 |
| #4502 | 2 |
| #4492 | 2 |
| #2245 | 3 |