Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 16. #807 | C4 | direct (N × H) |
| 17. C4×C3⋊C8 | C4 | semidirect |
| 68. C3⋊C8 | C42 | semidirect |
| 93. C3×C4 | #107 | semidirect |
| 129. C4 | #807 | direct (N × H) |
| 133. C3 | C4×#107 | 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×#807 | 2 |
| C4×C4⋊Dic3 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4529 | 2 |
| C4×#107 | 3 |