Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 4. #5500 | C2 | direct (N × H) |
| 5. C2×#890 | C2 | semidirect |
| 6. C2×#888 | C2 | semidirect |
| 21. #890 | C22 | semidirect |
| 22. #888 | C22 | semidirect |
| 31. C22×C3×C4 | Q8 | semidirect |
| 70. C2×C3×C4 | C2×Q8 | semidirect |
| 84. C22×C4 | Dic6 | semidirect |
| 121. C2×C4 | C2×Dic6 | semidirect |
| 125. C2×C3 | #544 | semidirect |
| 141. C3 | C2×#544 | semidirect |
| 143. C2 | #5500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C2×#926 | 2 |
| C2×#924 | 2 |
| #5500 | 2 |
| C2×#890 | 2 |
| C2×#888 | 2 |
| C2×#544 | 3 |