Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 163. C3 | #1653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5567 | 2 |
| #5020 | 2 |
| #4849 | 2 |
| #4680 | 2 |
| C3×Q8⋊C8 | 2 |
| #4486 | 2 |
| #4456 | 2 |
| #1653 | 3 |