Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 11. C3×C4×C8 | C4 | semidirect |
| 13. #817 | C4 | direct (N × H) |
| 37. C4×C8 | Dic3 | semidirect |
| 52. C3×C8 | C42 | semidirect |
| 71. C3×C4 | #106 | semidirect |
| 89. C8 | C4×Dic3 | semidirect |
| 100. C4 | #817 | direct (N × H) |
| 104. C3 | C4×#106 | semidirect |
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×#817 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4551 | 2 |
| C4×#106 | 3 |