Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
740 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 3. C22×Dic12 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4739 | C2 | direct (N × H) |
| 23. C2×Dic12 | C22 | semidirect |
| 25. #816 | C22 | semidirect |
| 81. C23×C3 | Q16 | semidirect |
| 139. C22×C3 | C2×Q16 | semidirect |
| 150. C23 | Dic12 | semidirect |
| 175. C2×C3 | #451 | semidirect |
| 184. C22 | C2×Dic12 | semidirect |
| 193. C3 | C2×#451 | semidirect |
| 195. C2 | #4739 | 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 |
| C2×#924 | 2 |
| C22×Dic12 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#816 | 2 |
| #4739 | 2 |
| C2×#451 | 3 |