Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 6. #4979 | C2 | direct (N × H) |
| 35. C22×C3×C4 | Q8 | semidirect |
| 44. C22×Dic3 | Q8 | semidirect |
| 81. C2×C3×C4 | C2×Q8 | semidirect |
| 89. C2×Dic3 | C2×Q8 | semidirect |
| 108. C22×C4 | Dic6 | semidirect |
| 153. C2×C4 | C2×Dic6 | semidirect |
| 155. C2×C3 | #395 | semidirect |
| 176. C3 | C2×#395 | semidirect |
| 177. C2 | #4979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×C3⋊#95 | 2 |
| #4979 | 2 |
| C2×#395 | 3 |