Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C4⋊Dic167 | C2 | semidirect |
| 2. #24923602 | C2 | semidirect |
| 3. #24923597 | C2 | semidirect |
| 4. #24923585 | C2 | semidirect |
| 5. #24923580 | C2 | semidirect |
| 6. #24923312 | C2 | semidirect |
| 7. #24923270 | C2 | semidirect |
| 8. #24923233 | C2 | semidirect |
| 18. #19128765 | C22 | semidirect |
| 19. #19128763 | C22 | semidirect |
| 20. #19128756 | C22 | semidirect |
| 21. #19128753 | C22 | semidirect |
| 130. C167 | #3092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic167 | 2 |
| #24923602 | 2 |
| #24923597 | 2 |
| #24923585 | 2 |
| #24923580 | 2 |
| #24923312 | 2 |
| #24923270 | 2 |
| #24923233 | 2 |
| #525×C167 | 2 |
| #3092 | 167 |