Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 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×#944 | C2 | semidirect |
| 4. #5672 | C2 | direct (N × H) |
| 5. C2×#879 | C2 | semidirect |
| 6. C2×#878 | C2 | semidirect |
| 7. C2×#870 | C2 | semidirect |
| 18. #944 | C22 | semidirect |
| 26. #879 | C22 | semidirect |
| 27. #878 | C22 | semidirect |
| 28. #870 | C22 | semidirect |
| 152. C2×C3 | #563 | semidirect |
| 166. C3 | C2×#563 | semidirect |
| 168. C2 | #5672 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#124 | 2 |
| C2×#944 | 2 |
| C2×#935 | 2 |
| #5672 | 2 |
| C2×#879 | 2 |
| C2×#878 | 2 |
| C2×#870 | 2 |
| C2×#563 | 3 |