Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 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 |
|---|---|---|
| 1. C23×Dic6 | C2 | semidirect |
| 3. C22×#204 | C2 | semidirect |
| 4. C2×C3×C22⋊C8 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4738 | C2 | direct (N × H) |
| 16. C22×Dic6 | C22 | semidirect |
| 23. C2×#204 | C22 | semidirect |
| 24. C3×C22⋊C8 | C22 | semidirect |
| 25. #816 | C22 | semidirect |
| 31. C2×C22⋊C8 | D3 | semidirect |
| 54. C2×Dic6 | D4 | semidirect |
| 79. C22⋊C8 | C2×D3 | semidirect |
| 82. C23×C3 | SD16 | semidirect |
| 107. Dic6 | C2×D4 | semidirect |
| 144. C22×C3 | C2×SD16 | semidirect |
| 162. C23 | #204 | semidirect |
| 186. C2×C3 | #448 | semidirect |
| 200. C22 | C2×#204 | semidirect |
| 208. C3 | C2×#448 | semidirect |
| 211. C2 | #4738 | 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×#930 | 2 |
| C22×#204 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#816 | 2 |
| #4738 | 2 |
| C2×#448 | 3 |