Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
888 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 429 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 |
|---|---|---|
| 5. #4975 | C2 | direct (N × H) |
| 17. C2×C4×Dic3 | C4 | semidirect |
| 42. C4×Dic3 | C2×C4 | semidirect |
| 64. C2×C3×C4 | C4⋊C4 | semidirect |
| 71. C2×Dic3 | C4⋊C4 | semidirect |
| 105. C3×C4 | C2×C4⋊C4 | semidirect |
| 107. Dic3 | C2×C4⋊C4 | semidirect |
| 124. C2×C4 | Dic3⋊C4 | semidirect |
| 128. C2×C3 | #384 | semidirect |
| 147. C4 | C2×Dic3⋊C4 | semidirect |
| 148. C3 | C2×#384 | semidirect |
| 149. C2 | #4975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| #4975 | 2 |
| C2×#384 | 3 |