Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 12. C3×#97 | C4 | semidirect |
| 13. C3×C4×C8 | C4 | semidirect |
| 39. #97 | Dic3 | semidirect |
| 40. C4×C8 | Dic3 | semidirect |
| 101. C3 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| C3⋊#338 | 2 |
| #4557 | 2 |
| #4556 | 2 |
| #4523 | 2 |
| #1841 | 3 |