Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#924 | C2 | semidirect |
| 3. C2×C3×C22⋊C8 | C2 | semidirect |
| 4. #5114 | C2 | semidirect |
| 5. #4738 | C2 | semidirect |
| 6. #4735 | C2 | semidirect |
| 7. #4731 | C2 | semidirect |
| 8. #4721 | C2 | semidirect |
| 13. C22×Dic6 | C22 | semidirect |
| 14. C22×C3×C8 | C22 | semidirect |
| 22. C2×C4⋊Dic3 | C22 | semidirect |
| 26. #924 | C22 | semidirect |
| 28. C2×#204 | C22 | semidirect |
| 30. C3×C22⋊C8 | C22 | semidirect |
| 31. #821 | C22 | semidirect |
| 32. #817 | C22 | semidirect |
| 33. #816 | C22 | semidirect |
| 41. C2×C22⋊C8 | D3 | semidirect |
| 81. C22×C8 | C2×D3 | semidirect |
| 99. C22⋊C8 | C2×D3 | semidirect |
| 102. C23×C3 | SD16 | semidirect |
| 195. C23 | #204 | semidirect |
| 251. C3 | #3187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C2×#924 | 2 |
| C2×C3×C22⋊C8 | 2 |
| #5114 | 2 |
| #4738 | 2 |
| #4735 | 2 |
| #4731 | 2 |
| #4721 | 2 |
| #3187 | 3 |