Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
238 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 177. C3 | #2097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#391 | 2 |
| C2×#835 | 2 |
| C2×#808 | 2 |
| C2×#807 | 2 |
| #4936 | 2 |
| #4524 | 2 |
| #2097 | 3 |