Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
244 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 11. #870 | C4 | semidirect |
| 12. #869 | C4 | semidirect |
| 28. C3×C42 | Q8 | semidirect |
| 71. C42 | Dic6 | semidirect |
| 111. C3 | #1995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×#376 | 2 |
| #4924 | 2 |
| #4523 | 2 |
| #1995 | 3 |