Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
200 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 141 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. #4457 | C2 | direct (N × H) |
| 20. C2×C3×C8 | C8 | semidirect |
| 49. C3×C8 | C2×C8 | semidirect |
| 57. C2×C8 | C3⋊C8 | semidirect |
| 88. C8 | C2×C3⋊C8 | semidirect |
| 89. C2×C3 | #334 | semidirect |
| 104. C3 | C2×#334 | semidirect |
| 105. C2 | #4457 | 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 |
| #4457 | 2 |
| C2×#334 | 3 |