Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #5122 | C2 | semidirect |
| 5. C2×C8×Dic3 | C2 | semidirect |
| 6. C3×#341 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 17. #907 | C4 | semidirect |
| 20. #825 | C4 | semidirect |
| 21. #821 | C4 | semidirect |
| 22. #816 | C4 | semidirect |
| 31. #341 | D3 | semidirect |
| 191. C3 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#907 | 2 |
| C2×#825 | 2 |
| #5122 | 2 |
| #5113 | 2 |
| C2×C8×Dic3 | 2 |
| C3×#341 | 2 |
| #4555 | 2 |
| #1764 | 3 |