Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×C3×C22⋊Q8 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 4. C23×C3⋊C8 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. #5048 | C2 | direct (N × H) |
| 7. C2×#809 | C2 | semidirect |
| 8. C2×#808 | C2 | semidirect |
| 15. C3×C22⋊Q8 | C22 | semidirect |
| 20. C2×#215 | C22 | semidirect |
| 28. C22×C3⋊C8 | C22 | semidirect |
| 29. #835 | C22 | semidirect |
| 30. #809 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 34. C2×C22⋊Q8 | D3 | semidirect |
| 71. C2×C3⋊C8 | D4 | semidirect |
| 85. C22⋊Q8 | C2×D3 | semidirect |
| 98. C23×C3 | SD16 | semidirect |
| 128. C3⋊C8 | C2×D4 | semidirect |
| 168. C22×C3 | C2×SD16 | semidirect |
| 188. C23 | #215 | semidirect |
| 216. C2×C3 | #465 | semidirect |
| 230. C22 | C2×#215 | semidirect |
| 240. C3 | C2×#465 | semidirect |
| 243. C2 | #5048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊Q8 | 2 |
| C22×#215 | 2 |
| C2×#930 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#835 | 2 |
| #5048 | 2 |
| C2×#809 | 2 |
| C2×#808 | 2 |
| C2×#465 | 3 |