Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 20. #888 | C4 | semidirect |
| 46. C3×C4⋊C4 | Q8 | semidirect |
| 50. C4⋊Dic3 | Q8 | semidirect |
| 123. C4⋊C4 | Dic6 | semidirect |
| 197. C3 | #1987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#888 | 2 |
| C2×Dic3⋊C8 | 2 |
| Dic3×C4⋊C4 | 2 |
| C3×#340 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| #1987 | 3 |