Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×C3×#97 | C2 | semidirect |
| 4. #5101 | C2 | semidirect |
| 6. #4552 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 17. #901 | C4 | semidirect |
| 21. #821 | C4 | semidirect |
| 22. #816 | C4 | semidirect |
| 25. #805 | C4 | semidirect |
| 30. C2×#97 | D3 | semidirect |
| 191. C3 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| C2×C3×#97 | 2 |
| #5113 | 2 |
| #5101 | 2 |
| C2×#805 | 2 |
| #4552 | 2 |
| #4523 | 2 |
| #1765 | 3 |