Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923824 | C2 | semidirect |
| 3. #24923606 | C2 | semidirect |
| 4. #24923546 | C2 | semidirect |
| 5. #24923475 | C2 | semidirect |
| 6. #24923474 | C2 | semidirect |
| 8. #24923368 | C2 | semidirect |
| 9. #24923366 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #474×C167 | C2 | semidirect |
| 16. #19128832 | C22 | semidirect |
| 21. #19128797 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. C4⋊(C167⋊C8) | C22 | semidirect |
| 33. #19128757 | C22 | semidirect |
| 34. #19128755 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 38. C4⋊Q8×C167 | C22 | semidirect |
| 40. #107×C167 | C22 | semidirect |
| 41. C4⋊C8×C167 | C22 | semidirect |
| 146. C167 | #3110 | semidirect |
| 152. #474 | D167 | semidirect |
| 164. C4⋊Q8 | C2×D167 | semidirect |
| 181. #107 | C2×D167 | semidirect |
| 183. C4⋊C8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923824 | 2 |
| C4×D4×D167 | 2 |
| #24923606 | 2 |
| #24923546 | 2 |
| #24923475 | 2 |
| #24923474 | 2 |
| #24923421 | 2 |
| #24923368 | 2 |
| #24923366 | 2 |
| #24923325 | 2 |
| #474×C167 | 2 |
| #3110 | 167 |