Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 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. C4×Dic6 | C4 | semidirect |
| 18. #810 | C4 | direct (N × H) |
| 79. Dic6 | C42 | semidirect |
| 110. C3×C4 | #103 | semidirect |
| 151. C4 | #810 | direct (N × H) |
| 155. C3 | C4×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C3×C4×C4⋊C4 | 2 |
| C2×#810 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4529 | 2 |
| C4×#103 | 3 |