Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 125 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. #4480 | C2 | direct (N × H) |
| 33. C2×C3⋊C8 | C8 | semidirect |
| 62. C3⋊C8 | C2×C8 | semidirect |
| 106. C2×C3 | #334 | semidirect |
| 122. C3 | C2×#334 | semidirect |
| 123. C2 | #4480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊C8 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4480 | 2 |
| C2×#334 | 3 |