Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1112 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C3×C22⋊C4 | C2 | semidirect |
| 3. C22×#217 | C2 | semidirect |
| 4. C2×#806 | C2 | direct (N × H) |
| 7. C24×D3 | C4 | semidirect |
| 13. C22×#67 | C4 | semidirect |
| 16. C23×Dic3 | C4 | semidirect |
| 18. C2×C3×C22⋊C4 | C22 | semidirect |
| 20. C2×#217 | C22 | semidirect |
| 21. #806 | C22 | direct (N × H) |
| 24. C22×C22⋊C4 | D3 | semidirect |
| 37. C23×D3 | C2×C4 | semidirect |
| 47. C2×#67 | C2×C4 | semidirect |
| 53. C22×Dic3 | C2×C4 | semidirect |
| 55. C3×C22⋊C4 | C23 | semidirect |
| 57. #217 | C23 | semidirect |
| 72. C2×C22⋊C4 | C2×D3 | semidirect |
| 98. C22×D3 | C22×C4 | semidirect |
| 109. C2×Dic3 | C22×C4 | semidirect |
| 141. C22⋊C4 | C22×D3 | semidirect |
| 153. C22×C3 | #99 | semidirect |
| 210. C2×C3 | C2×#99 | semidirect |
| 228. C22 | #806 | direct (N × H) |
| 239. C3 | C22×#99 | semidirect |
| 247. C2 | C2×#806 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#67 | 2 |
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C2×#806 | 2 |
| C22×#99 | 3 |