Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. #24923607 | C2 | semidirect |
| 3. #24923566 | C2 | semidirect |
| 4. #24923471 | C2 | semidirect |
| 6. #24923367 | C2 | semidirect |
| 7. C4×#14581937 | C2 | semidirect |
| 8. #24923330 | C2 | semidirect |
| 9. #541×C167 | C2 | semidirect |
| 18. #19128765 | C22 | semidirect |
| 19. #19128763 | C22 | semidirect |
| 20. C4⋊(C167⋊C8) | C22 | semidirect |
| 21. #19128756 | C22 | semidirect |
| 22. #19128756 | C22 | semidirect |
| 26. #19128743 | C22 | semidirect |
| 27. C4×C167⋊C8 | C22 | semidirect |
| 28. C4⋊Q8×C167 | C22 | semidirect |
| 31. #125×C167 | C22 | semidirect |
| 33. C4×Q8×C167 | C22 | semidirect |
| 102. C167 | #3123 | semidirect |
| 104. #541 | D167 | semidirect |
| 116. C4⋊Q8 | C2×D167 | semidirect |
| 119. #125 | C2×D167 | semidirect |
| 121. C4×Q8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923743 | 2 |
| #24923607 | 2 |
| #24923566 | 2 |
| #24923471 | 2 |
| #24923419 | 2 |
| #24923367 | 2 |
| C4×#14581937 | 2 |
| #24923330 | 2 |
| #541×C167 | 2 |
| #3123 | 167 |