Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4⋊C4×D167 | C2 | semidirect |
| 3. #24923606 | C2 | semidirect |
| 4. #24923601 | C2 | semidirect |
| 5. #24923589 | C2 | semidirect |
| 6. #24923584 | C2 | semidirect |
| 7. #24923312 | C2 | semidirect |
| 8. #24923271 | C2 | semidirect |
| 9. #24923268 | C2 | semidirect |
| 10. #24923232 | C2 | semidirect |
| 11. #428×C167 | C2 | semidirect |
| 30. #19128765 | C22 | semidirect |
| 31. #19128763 | C22 | semidirect |
| 32. #19128757 | C22 | semidirect |
| 33. #19128755 | C22 | semidirect |
| 34. #19128754 | C22 | semidirect |
| 35. #19128752 | C22 | semidirect |
| 41. #107×C167 | C22 | semidirect |
| 42. #106×C167 | C22 | semidirect |
| 155. C167 | #3092 | semidirect |
| 164. #428 | D167 | semidirect |
| 190. #107 | C2×D167 | semidirect |
| 192. #106 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923781 | 2 |
| C2×C4⋊C4×D167 | 2 |
| #24923606 | 2 |
| #24923601 | 2 |
| #24923589 | 2 |
| #24923584 | 2 |
| #24923312 | 2 |
| #24923271 | 2 |
| #24923268 | 2 |
| #24923232 | 2 |
| #428×C167 | 2 |
| #3092 | 167 |