Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 219. C3 | #3374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5570 | 2 |
| #5567 | 2 |
| C3×C4×Q16 | 2 |
| #5182 | 2 |
| #5031 | 2 |
| #5020 | 2 |
| #4877 | 2 |
| #4797 | 2 |
| #4789 | 2 |
| #4681 | 2 |
| #4679 | 2 |
| #3374 | 3 |