Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 16. #890 | C4 | semidirect |
| 17. #888 | C4 | semidirect |
| 41. C3×C42 | Q8 | semidirect |
| 52. C4×Dic3 | Q8 | semidirect |
| 114. C42 | Dic6 | semidirect |
| 166. C3 | #1995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5517 | 2 |
| #5118 | 2 |
| #4932 | 2 |
| C3×#339 | 2 |
| #4555 | 2 |
| #4532 | 2 |
| #4523 | 2 |
| #1995 | 3 |