Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
752 conjugacy classes of subgroups; only the 421 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 421 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 |
|---|---|---|
| 4. C4×C4⋊Dic3 | C2 | semidirect |
| 5. #4932 | C2 | semidirect |
| 6. C42×Dic3 | C2 | semidirect |
| 10. C2×C3×C42 | C4 | semidirect |
| 15. #926 | C4 | direct (N × H) |
| 40. C4⋊Dic3 | C2×C4 | semidirect |
| 42. C4×Dic3 | C2×C4 | semidirect |
| 50. C2×C42 | Dic3 | semidirect |
| 61. C2×C3×C4 | C42 | semidirect |
| 97. C3×C4 | #117 | semidirect |
| 107. C2×C4 | C4×Dic3 | semidirect |
| 129. C4 | #926 | direct (N × H) |
| 130. C3 | C4×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C42 | 2 |
| C2×#926 | 2 |
| C4×#217 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4932 | 2 |
| C42×Dic3 | 2 |
| C4×#117 | 3 |