Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 14. #815 | C4 | semidirect |
| 15. C8×Dic3 | C4 | semidirect |
| 43. #97 | Dic3 | semidirect |
| 45. C4×C8 | Dic3 | semidirect |
| 105. C3 | #1747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#405 | 2 |
| #5101 | 2 |
| C3⋊#338 | 2 |
| #4557 | 2 |
| #4531 | 2 |
| #1747 | 3 |