Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 17. C4⋊(C3⋊C8) | C4 | semidirect |
| 107. C3×C4 | #106 | semidirect |
| 154. C4 | #808 | semidirect |
| 159. C3 | #1948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊C4 | 2 |
| C2×#808 | 2 |
| #4935 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4529 | 2 |
| #1948 | 3 |