Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5825 | C2 | semidirect |
| 3. #5234 | C2 | semidirect |
| 4. #5218 | C2 | semidirect |
| 5. #5042 | C2 | semidirect |
| 6. #5041 | C2 | semidirect |
| 7. #5040 | C2 | semidirect |
| 8. #5035 | C2 | semidirect |
| 9. #4996 | C2 | semidirect |
| 13. C22×Dic6 | C22 | semidirect |
| 27. #926 | C22 | semidirect |
| 29. #924 | C22 | semidirect |
| 30. C2×#208 | C22 | semidirect |
| 31. C22×C3⋊C8 | C22 | semidirect |
| 35. #830 | C22 | semidirect |
| 36. #810 | C22 | semidirect |
| 37. #810 | C22 | semidirect |
| 38. #808 | C22 | semidirect |
| 39. #807 | C22 | semidirect |
| 268. C3 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5825 | 2 |
| #5234 | 2 |
| #5218 | 2 |
| #5042 | 2 |
| #5041 | 2 |
| #5040 | 2 |
| #5035 | 2 |
| #4996 | 2 |
| #3200 | 3 |